I am looking for a modern and thorough exposition for presentations of groups
3
$begingroup$
Conider the following abstract description for the Quaternion group:
$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$
This description is called a presentation of the Quaternion group via generators and relations.
I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?
Thank you for your ideas!
group-theory reference-request soft-question big-list group-presentation
edited Dec 18 '18 at 15:55
Tortoise
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
$endgroup$
|
show 2 more comments
3
$begingroup$
Conider the following abstract description for the Quaternion group:
$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$
This description is called a presentation of the Quaternion group via generators and relations.
I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?
Thank you for your ideas!
group-theory reference-request soft-question big-list group-presentation
edited Dec 18 '18 at 15:55
Tortoise
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
$endgroup$
2
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
3
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
2
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23
|
show 2 more comments
3
3
3
1
$begingroup$
Conider the following abstract description for the Quaternion group:
$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$
This description is called a presentation of the Quaternion group via generators and relations.
I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?
Thank you for your ideas!
group-theory reference-request soft-question big-list group-presentation
edited Dec 18 '18 at 15:55
Tortoise
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
$endgroup$
Conider the following abstract description for the Quaternion group:
$$langle x,ymid x^{4}=1,x^{2}=y^{2},y^{-1}xy=x^{-1}rangle$$
This description is called a presentation of the Quaternion group via generators and relations.
I am looking for a modern and thorough exposition for presentations of groups because I think it is a fascinating area about which I would like to know more. Are there any books or comprehensive online sources that you could recommend?
Thank you for your ideas!
group-theory reference-request soft-question big-list group-presentation
group-theory reference-request soft-question big-list group-presentation
edited Dec 18 '18 at 15:55
Tortoise
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
edited Dec 18 '18 at 15:55
Tortoise
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
edited Dec 18 '18 at 15:55
Tortoise
323112
edited Dec 18 '18 at 15:55
Tortoise
323112
edited Dec 18 '18 at 15:55
Tortoise
323112
323112
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
asked Dec 16 '18 at 14:49
MoritzMoritz
1,2681723
1,2681723
2
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
3
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
2
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23
|
show 2 more comments
2
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
3
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
2
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23
2
2
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
3
3
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
2
2
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23
|
show 2 more comments
1 Answer
1
active
oldest
votes
2
$begingroup$
The answer occurs in the comments above. I summarize
- "Combinatorial Group Theory: Presentations of Groups in Terms of
Generators and Relations" by W. Magnus and others, 444 pages, ISBN
0486438309, 2004-reprint of 1976-edition - "Presentations of Groups,
2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
1997-edition - "Topics in the theory of group presentations" by D. L.
Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042690%2fi-am-looking-for-a-modern-and-thorough-exposition-for-presentations-of-groups%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
2
$begingroup$
The answer occurs in the comments above. I summarize
- "Combinatorial Group Theory: Presentations of Groups in Terms of
Generators and Relations" by W. Magnus and others, 444 pages, ISBN
0486438309, 2004-reprint of 1976-edition - "Presentations of Groups,
2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
1997-edition - "Topics in the theory of group presentations" by D. L.
Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
$endgroup$
add a comment |
2
$begingroup$
The answer occurs in the comments above. I summarize
- "Combinatorial Group Theory: Presentations of Groups in Terms of
Generators and Relations" by W. Magnus and others, 444 pages, ISBN
0486438309, 2004-reprint of 1976-edition - "Presentations of Groups,
2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
1997-edition - "Topics in the theory of group presentations" by D. L.
Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
$endgroup$
add a comment |
2
2
2
$begingroup$
The answer occurs in the comments above. I summarize
- "Combinatorial Group Theory: Presentations of Groups in Terms of
Generators and Relations" by W. Magnus and others, 444 pages, ISBN
0486438309, 2004-reprint of 1976-edition - "Presentations of Groups,
2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
1997-edition - "Topics in the theory of group presentations" by D. L.
Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
$endgroup$
The answer occurs in the comments above. I summarize
- "Combinatorial Group Theory: Presentations of Groups in Terms of
Generators and Relations" by W. Magnus and others, 444 pages, ISBN
0486438309, 2004-reprint of 1976-edition - "Presentations of Groups,
2ed" by D.L. Johnson, 232 pages, ISBN 0521585422, 2008-reprint of
1997-edition - "Topics in the theory of group presentations" by D. L.
Johnson, 311 pages, ISBN 9780521231084, 2008-reprint of 1980-edition
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
answered Dec 18 '18 at 15:37
TortoiseTortoise
323112
323112
add a comment |
add a comment |
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042690%2fi-am-looking-for-a-modern-and-thorough-exposition-for-presentations-of-groups%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
Dear Moritz, almost every book on group theory has a chapter on presentation of groups, free groups, free products of groups and so on :) Perhaps you like my lecture notes, in particular chapter $4$ and its references.
$endgroup$
– Dietrich Burde
Dec 16 '18 at 16:38
$begingroup$
@Dietrich Burde: Thank you for your kind response. I know that books about group theory have often small chapters (in general about 10 pages long) about this topic or treat it as a secondary subject. I was looking more for a "monograph" about presentations - if such a thing exists. I also found lecture notes from a course by Derek Holt about the theme but they were taken by a student and were full of errors. So, my question is about a good personal recommendation that someone could give me: comprehensive, modern and - if possible - error free. A book is good, an online source even better.
$endgroup$
– Moritz
Dec 17 '18 at 15:39
3
$begingroup$
Have you looked at Presentation of groups by Johnson, or any book on/titled Combinatorial group theory?
$endgroup$
– Paul Plummer
Dec 17 '18 at 17:48
2
$begingroup$
Possible duplicate of Combinatorial group theory books
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:20
$begingroup$
While I voted to close as duplicate it is worth pointing out that combinatorial group theory is very influenced nowadays by geometric group theory, so it is also worth looking into that. Check out this question for that
$endgroup$
– Paul Plummer
Dec 17 '18 at 20:23