Order and sign of a cycle
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I would usually show workings or attempts of a method when posting a question here, but for this I am completely lost. I don't believe it to be a very hard question but it is as follows:
Determine the order and the sign of $(5,6,7,8,9)(3,4,5,6)(2,3,4)(1,2)$ in $S_9$.
(Each number is separate i.e. the first is 5,6,7,8 and 9 but I wasn't sure of how to create a horizontal space).
I appreciate any help offered, even if it is just a hint.
group-theory permutation-cycles
edited Dec 5 '18 at 18:31
Bernard
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
$endgroup$
add a comment |
$begingroup$
I would usually show workings or attempts of a method when posting a question here, but for this I am completely lost. I don't believe it to be a very hard question but it is as follows:
Determine the order and the sign of $(5,6,7,8,9)(3,4,5,6)(2,3,4)(1,2)$ in $S_9$.
(Each number is separate i.e. the first is 5,6,7,8 and 9 but I wasn't sure of how to create a horizontal space).
I appreciate any help offered, even if it is just a hint.
group-theory permutation-cycles
edited Dec 5 '18 at 18:31
Bernard
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
$endgroup$
add a comment |
$begingroup$
I would usually show workings or attempts of a method when posting a question here, but for this I am completely lost. I don't believe it to be a very hard question but it is as follows:
Determine the order and the sign of $(5,6,7,8,9)(3,4,5,6)(2,3,4)(1,2)$ in $S_9$.
(Each number is separate i.e. the first is 5,6,7,8 and 9 but I wasn't sure of how to create a horizontal space).
I appreciate any help offered, even if it is just a hint.
group-theory permutation-cycles
edited Dec 5 '18 at 18:31
Bernard
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
$endgroup$
I would usually show workings or attempts of a method when posting a question here, but for this I am completely lost. I don't believe it to be a very hard question but it is as follows:
Determine the order and the sign of $(5,6,7,8,9)(3,4,5,6)(2,3,4)(1,2)$ in $S_9$.
(Each number is separate i.e. the first is 5,6,7,8 and 9 but I wasn't sure of how to create a horizontal space).
I appreciate any help offered, even if it is just a hint.
group-theory permutation-cycles
group-theory permutation-cycles
edited Dec 5 '18 at 18:31
Bernard
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
edited Dec 5 '18 at 18:31
Bernard
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
edited Dec 5 '18 at 18:31
Bernard
120k740114
edited Dec 5 '18 at 18:31
Bernard
120k740114
edited Dec 5 '18 at 18:31
Bernard
120k740114
120k740114
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
asked Dec 5 '18 at 18:02
basic_ceremonybasic_ceremony
53
53
add a comment |
add a comment |
1 Answer
1
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oldest
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Hint: Write your element of $S_9$ as the product of disjoint cycles. For instance, one of those cycles will be $(1 4 2)$.
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
$endgroup$
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
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That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
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active
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active
oldest
votes
$begingroup$
Hint: Write your element of $S_9$ as the product of disjoint cycles. For instance, one of those cycles will be $(1 4 2)$.
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
$endgroup$
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
add a comment |
$begingroup$
Hint: Write your element of $S_9$ as the product of disjoint cycles. For instance, one of those cycles will be $(1 4 2)$.
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
$endgroup$
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
add a comment |
$begingroup$
Hint: Write your element of $S_9$ as the product of disjoint cycles. For instance, one of those cycles will be $(1 4 2)$.
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
$endgroup$
Hint: Write your element of $S_9$ as the product of disjoint cycles. For instance, one of those cycles will be $(1 4 2)$.
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
answered Dec 5 '18 at 18:05
José Carlos SantosJosé Carlos Santos
159k22126231
159k22126231
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
add a comment |
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
Thanks! Would the product of disjoint cycles be given by (1 4 2)(3 6)(5 7 8 9) by any chance?
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:16
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
That is correct!
$endgroup$
– José Carlos Santos
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
$begingroup$
Aha! Thank you very much, sir.
$endgroup$
– basic_ceremony
Dec 5 '18 at 18:17
add a comment |
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