Question

Show for $\alpha\in S_n$, $\alpha^{-1}(123)\alpha=(xyz)$ for some $x,y,z$. How are $x,y,z$ related to $\alpha$? Generalize.

score 75 · Answer 1 · 2021-04-29 13:04:25

75

Views

Show for $\alpha\in S_n$, $\alpha^{-1}(123)\alpha=(xyz)$ for some $x,y,z$. How are $x,y,z$ related to $\alpha$? Generalize.

Published on 29 Apr 2021 - 13:04

score 64 · Answer 2 · 2021-05-04 19:54:23

64

Views

How $\beta$ and $\gamma$ are related to conjugation

Published on 04 May 2021 - 19:54

score 85 · Answer 3 · 2021-05-06 22:30:30

85

Views

For which $n\geq2$ does there exist $\sigma \in A_n$ with $|\sigma|>n$?

Published on 06 May 2021 - 22:30

score 54 · Answer 4 · 2021-05-10 17:45:49

54

Views

Applying Burnside Lemma to board game

Published on 10 May 2021 - 17:45

score 433 · Answer 5 · 2021-05-11 09:22:31

433

Views

Show that all order $n$ elements of $S_n$ are $n$-cycles if and only if $n=p^r$, $p$ prime

Published on 11 May 2021 - 9:22

score 705 · Answer 6 · 2021-05-17 02:29:38

705

Views

If a normal subgroup $N$ of $A_n$ contains any $3$-cycle, then $N = A_n$

Published on 17 May 2021 - 2:29

score 1.4k · Answer 7 · 2021-05-17 22:22:32

1.4k

Views

Every element of $S_n$ can be written as a product of transpositions of the form $(1 i )$, for various $i$

Published on 17 May 2021 - 22:22

score 240 · Answer 8 · 2021-05-19 19:31:21

240

Views

In $S_7$, describe the conjugates of $(1 2)(3 4 5)$

Published on 19 May 2021 - 19:31

score 42 · Answer 9 · 2021-05-22 15:36:36

42

Views

Intransitivity of a group generated by two 2-cycles (1 2), (3 4)

Published on 22 May 2021 - 15:36

score 34 · Answer 10 · 2021-05-23 10:56:41

34

Views

Writing permutations as products of disjoint cycles (left to right)

Published on 23 May 2021 - 10:56

score 369 · Answer 11 · 2021-05-23 13:57:22

369

Views

What is the maximum number of shuffles required for the cards to return to their original position?

Published on 23 May 2021 - 13:57

score 257 · Answer 12 · 2021-05-26 09:08:03

257

Views

Every element in An is product of n-cycles

Published on 26 May 2021 - 9:08

score 81 · Answer 13 · 2021-05-29 15:55:48

81

Views

Prove that $\tau \sigma \tau ^{-1}$ depends only on the lateral class of $\tau$ with respect to $Z(\sigma)$

Published on 29 May 2021 - 15:55

score 225 · Answer 14 · 2021-05-31 14:21:19

225

Views

Find the conjugacy class in $S_n$ of $(12...n)$. What is the order of the centalizer of $(12...n)$ in $S_n$?

Published on 31 May 2021 - 14:21

score 1.4k · Answer 15 · 2021-06-01 03:26:55

1.4k

Views

Algorithm for finding the cycle-decomposition of a permutation.

Published on 01 Jun 2021 - 3:26

List Question

Show for $\alpha\in S_n$, $\alpha^{-1}(123)\alpha=(xyz)$ for some $x,y,z$. How are $x,y,z$ related to $\alpha$? Generalize.

How $\beta$ and $\gamma$ are related to conjugation

For which $n\geq2$ does there exist $\sigma \in A_n$ with $|\sigma|>n$?

Applying Burnside Lemma to board game

Show that all order $n$ elements of $S_n$ are $n$-cycles if and only if $n=p^r$, $p$ prime

If a normal subgroup $N$ of $A_n$ contains any $3$-cycle, then $N = A_n$

Every element of $S_n$ can be written as a product of transpositions of the form $(1 i )$, for various $i$

In $S_7$, describe the conjugates of $(1 2)(3 4 5)$

Intransitivity of a group generated by two 2-cycles (1 2), (3 4)

Writing permutations as products of disjoint cycles (left to right)

What is the maximum number of shuffles required for the cards to return to their original position?

Every element in An is product of n-cycles

Prove that $\tau \sigma \tau ^{-1}$ depends only on the lateral class of $\tau$ with respect to $Z(\sigma)$

Find the conjugacy class in $S_n$ of $(12...n)$. What is the order of the centalizer of $(12...n)$ in $S_n$?

Algorithm for finding the cycle-decomposition of a permutation.

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