Presentations of $D_8$ using permutations
0
$begingroup$
I fond a lot of examples using presentation of $D_8$ by generators which are permutations of $S_4$.
1) How many presentations could be found?
2) Could it be presented by permutations of $S_5$ or any different group?
Thanks for advance
abstract-algebra group-theory finite-groups permutations group-presentation
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
$endgroup$
|
show 10 more comments
0
$begingroup$
I fond a lot of examples using presentation of $D_8$ by generators which are permutations of $S_4$.
1) How many presentations could be found?
2) Could it be presented by permutations of $S_5$ or any different group?
Thanks for advance
abstract-algebra group-theory finite-groups permutations group-presentation
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
$endgroup$
$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47
|
show 10 more comments
0
0
0
$begingroup$
I fond a lot of examples using presentation of $D_8$ by generators which are permutations of $S_4$.
1) How many presentations could be found?
2) Could it be presented by permutations of $S_5$ or any different group?
Thanks for advance
abstract-algebra group-theory finite-groups permutations group-presentation
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
$endgroup$
I fond a lot of examples using presentation of $D_8$ by generators which are permutations of $S_4$.
1) How many presentations could be found?
2) Could it be presented by permutations of $S_5$ or any different group?
Thanks for advance
abstract-algebra group-theory finite-groups permutations group-presentation
abstract-algebra group-theory finite-groups permutations group-presentation
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
asked Dec 5 '18 at 10:23
A.MessabA.Messab
527
527
$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47
|
show 10 more comments
$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47
$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47
|
show 10 more comments
0
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$begingroup$
What counts as different presentations?
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:36
$begingroup$
@TobiasKildetoft they don´t look the same!
$endgroup$
– A.Messab
Dec 5 '18 at 10:39
$begingroup$
Then there will be infinitely many presentations, since I can just keep adding new relations.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:40
$begingroup$
@TobiasKildetoft It´s not like one is equipped with more relationd than the other, it´s about seeing a different sets of generators plus different sets of relators, and by different I mean looks different not just sized differently
$endgroup$
– A.Messab
Dec 5 '18 at 10:44
$begingroup$
I think you may want to look up the definition of a presentation, because it does mean what you seem to be using it to mean here.
$endgroup$
– Tobias Kildetoft
Dec 5 '18 at 10:47