Question

Determine the least positive integer $n$ for which the cyclic group $(\Bbb Z_{60},+\pmod{60})$ is isomorphic to a subgroup of $S_n$.

score 92 · Answer 1 · 2019-11-21 01:52:43

92

Views

Determine the least positive integer $n$ for which the cyclic group $(\Bbb Z_{60},+\pmod{60})$ is isomorphic to a subgroup of $S_n$.

Published on 21 Nov 2019 - 1:52

score 100 · Answer 2 · 2026-03-26 04:51:05

100

Views

Convoluted permutation conjugate proof but is it sound?

Published on 26 Mar 2026 - 4:51

score 79 · Answer 3 · 2019-11-22 21:30:11

79

Views

Prove that in a group of permutation $S_7$ every two elements with order $10$ are conjugated. Prove that this fact is not truth in $S_9$.

Published on 22 Nov 2019 - 21:30

score 33 · Answer 4 · 2019-11-24 13:03:11

33

Views

$S_n$ symmetric group of order n and elements of order n

Published on 24 Nov 2019 - 13:03

score 198 · Answer 5 · 2026-03-25 22:06:02

198

Views

Generating an infinite group of symmetries with an element of order 2 and 4

Published on 25 Mar 2026 - 22:06

score 80 · Answer 6 · 2026-03-26 12:50:11

80

Views

Find a nonabelian subgroup $T$ of $S_3 \times \Bbb Z_4$ of index $2$, generated by elements $x,y$ such that $|x|=6$, $x^3=y^2$, and $yx=x^{-1}y$.

Published on 26 Mar 2026 - 12:50

score 1.6k · Answer 7 · 2019-11-26 09:37:44

1.6k

Views

Am I able to calculate the character table of A4 without using the character table of S4?

Published on 26 Nov 2019 - 9:37

score 42 · Answer 8 · 2026-03-26 03:11:24

42

Views

Does there exist any $x\in S_{10}$ such that $x(1\ \ 2\ \ 3)x=(9\ \ 10)$?

Published on 26 Mar 2026 - 3:11

score 232 · Answer 9 · 2019-11-29 17:05:00

232

Views

Conjugacy class of transpositions of a finite set $E$

Published on 29 Nov 2019 - 17:05

score 38 · Answer 10 · 2019-11-29 20:53:07

38

Views

Action of $\mathfrak{S}_n$ on the additive group of mappings from $\mathbb{Z}^{[1,n]}$ to $\mathbb{Z}$ and inversions of elements of $\mathfrak{S}_n$

Published on 29 Nov 2019 - 20:53

score 587 · Answer 11 · 2019-11-29 23:19:20

587

Views

Normal subgroups of $S_n$ and even permutations

Published on 29 Nov 2019 - 23:19

score 119 · Answer 12 · 2019-11-30 16:34:04

119

Views

Cayley's Theorem and proving $S_n$ is isomorphic to a group of permutations.

Published on 30 Nov 2019 - 16:34

score 34 · Answer 13 · 2019-11-30 16:48:43

34

Views

Set description of the group generated by a family of transpositions

Published on 30 Nov 2019 - 16:48

score 36 · Answer 14 · 2019-12-01 01:02:28

36

Views

Calculating amount of Sylow 2-subgroups in $S_5$ by using the amounts of 3- and 5- subgroups?

Published on 01 Dec 2019 - 1:02

score 339 · Answer 15 · 2019-12-01 20:17:18

339

Views

The action of $S_5$ on $6$ points

Published on 01 Dec 2019 - 20:17

List Question

Determine the least positive integer $n$ for which the cyclic group $(\Bbb Z_{60},+\pmod{60})$ is isomorphic to a subgroup of $S_n$.

Convoluted permutation conjugate proof but is it sound?

Prove that in a group of permutation $S_7$ every two elements with order $10$ are conjugated. Prove that this fact is not truth in $S_9$.

$S_n$ symmetric group of order n and elements of order n

Generating an infinite group of symmetries with an element of order 2 and 4

Find a nonabelian subgroup $T$ of $S_3 \times \Bbb Z_4$ of index $2$, generated by elements $x,y$ such that $|x|=6$, $x^3=y^2$, and $yx=x^{-1}y$.

Am I able to calculate the character table of A4 without using the character table of S4?

Does there exist any $x\in S_{10}$ such that $x(1\ \ 2\ \ 3)x=(9\ \ 10)$?

Conjugacy class of transpositions of a finite set $E$

Action of $\mathfrak{S}_n$ on the additive group of mappings from $\mathbb{Z}^{[1,n]}$ to $\mathbb{Z}$ and inversions of elements of $\mathfrak{S}_n$

Normal subgroups of $S_n$ and even permutations

Cayley's Theorem and proving $S_n$ is isomorphic to a group of permutations.

Set description of the group generated by a family of transpositions

Calculating amount of Sylow 2-subgroups in $S_5$ by using the amounts of 3- and 5- subgroups?

The action of $S_5$ on $6$ points

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