Question

$n\ge 5$, prove $A_n$ is the only non-trivial proper normal subgroup of $S_n$.

score 125 · Answer 1 · 2026-03-27 00:10:24

125

Views

$n\ge 5$, prove $A_n$ is the only non-trivial proper normal subgroup of $S_n$.

Published on 27 Mar 2026 - 0:10

score 138 · Answer 2 · 2023-11-27 18:08:46

138

Views

Interpretation of 1089-number trick in terms of symmetric group action on Ext-group?

Published on 27 Nov 2023 - 18:08

score 1k · Answer 3 · 2023-11-27 22:10:16

1k

Views

Test if a finite group is a symmetric group algorithmically

Published on 27 Nov 2023 - 22:10

score 54 · Answer 4 · 2023-11-28 18:16:06

54

Views

Does this group $S=\bigcup_{i=1}^{\infty} S_n$ have a name?

Published on 28 Nov 2023 - 18:16

score 100 · Answer 5 · 2023-12-01 00:34:41

100

Views

Natural way of inducing sequence of subgroups of $S_n$

Published on 01 Dec 2023 - 0:34

score 41 · Answer 6 · 2026-03-31 15:44:13

41

Views

Connection between permutations and rank–nullity?

Published on 31 Mar 2026 - 15:44

score 42 · Answer 7 · 2026-03-25 07:46:20

42

Views

What is analogous to the set of four main diagonals in Rotational Symmetry of Cube, if we want to find the total symmetry of cube?

Published on 25 Mar 2026 - 7:46

score 150 · Answer 8 · 2023-12-07 08:27:22

150

Views

Let $A$ be an abelian group of order $2^{100}$. Prove that $A$ is not a subgroup of $S_n$ for $n<200$.

Published on 07 Dec 2023 - 8:27

score 76 · Answer 9 · 2023-12-07 17:05:53

76

Views

Is the class of all symmetric groups an elementary class?

Published on 07 Dec 2023 - 17:05

score 33 · Answer 10 · 2026-03-20 23:43:22

33

Views

N-dimensional linear representation of symmetric group S(N)

Published on 20 Mar 2026 - 23:43

score 79 · Answer 11 · 2023-12-09 22:50:47

79

Views

Is it possible to define $S_n$ with a transposition series?

Published on 09 Dec 2023 - 22:50

score 186 · Answer 12 · 2026-03-26 08:03:32

186

Views

Transitive Galois action on the set of prime ideals

Published on 26 Mar 2026 - 8:03

score 135 · Answer 13 · 2023-12-12 00:23:10

135

Views

What is the least positive integer $n > 1$ such that $x^n$ and $x$ are conjugate, for every $ x\in S_{11}$

Published on 12 Dec 2023 - 0:23

score 269 · Answer 14 · 2023-12-16 03:32:34

269

Views

An Interesting Type of Infinite Permutation Group

Published on 16 Dec 2023 - 3:32

score 394 · Answer 15 · 2026-03-27 01:47:40

394

Views

Number of permutations in the symmetric group $S_n$ composed of $k$ disjoint $m$-cycles

Published on 27 Mar 2026 - 1:47

List Question

$n\ge 5$, prove $A_n$ is the only non-trivial proper normal subgroup of $S_n$.

Interpretation of 1089-number trick in terms of symmetric group action on Ext-group?

Test if a finite group is a symmetric group algorithmically

Does this group $S=\bigcup_{i=1}^{\infty} S_n$ have a name?

Natural way of inducing sequence of subgroups of $S_n$

Connection between permutations and rank–nullity?

What is analogous to the set of four main diagonals in Rotational Symmetry of Cube, if we want to find the total symmetry of cube?

Let $A$ be an abelian group of order $2^{100}$. Prove that $A$ is not a subgroup of $S_n$ for $n<200$.

Is the class of all symmetric groups an elementary class?

N-dimensional linear representation of symmetric group S(N)

Is it possible to define $S_n$ with a transposition series?

Transitive Galois action on the set of prime ideals

What is the least positive integer $n > 1$ such that $x^n$ and $x$ are conjugate, for every $ x\in S_{11}$

An Interesting Type of Infinite Permutation Group

Number of permutations in the symmetric group $S_n$ composed of $k$ disjoint $m$-cycles

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