Question

A permutation in $S_n$ whose cycle decomposition contains a transposition

score 407 · Answer 1 · 2019-01-14 21:58:51

407

Views

A permutation in $S_n$ whose cycle decomposition contains a transposition

Published on 14 Jan 2019 - 21:58

score 1.1k · Answer 2 · 2026-03-25 06:07:01

1.1k

Views

Which of these numbers could be the exact number of elements of order $21$ in a group?

Published on 25 Mar 2026 - 6:07

score 115 · Answer 3 · 2026-03-29 12:40:14

115

Views

When is a group homomorphism “extendable”?

Published on 29 Mar 2026 - 12:40

score 1.6k · Answer 4 · 2019-01-15 23:43:48

1.6k

Views

Let $p,q$ be odd primes. Prove that a group of order $2 pq$ is solvable.

Published on 15 Jan 2019 - 23:43

score 334 · Answer 5 · 2026-03-26 12:37:06

334

Views

Group generated by $(1234567)$ and $(26)(34)$ is of order 168.

Published on 26 Mar 2026 - 12:37

score 1.4k · Answer 6 · 2019-01-16 11:51:58

Let $G$ be finite and every nonidentity element have prime order. If $Z(G)\neq\{e\}$, prove that every nonidentity element of $G$ has the same order.

score 234 · Answer 7 · 2026-03-25 07:43:51

234

Views

Computing the class-preserving automorphism group of finite $p$-groups

Published on 25 Mar 2026 - 7:43

score 166 · Answer 8 · 2026-03-25 18:47:36

166

Views

Number of automorphisms on alternating group $A_n$.

Published on 25 Mar 2026 - 18:47

score 75 · Answer 9 · 2019-01-17 12:39:40

75

Views

Conjugacy classes in special linear groups over $\mathbb{Z}/p^k$

Published on 17 Jan 2019 - 12:39

score 4.4k · Answer 10 · 2026-03-27 12:28:57

4.4k

Views

Prove that a finite Abelian group $G$ is not cyclic if and only if it contains a subgroup isomorphic to $\mathbb{Z}_p\times\mathbb{Z}_p$

Published on 27 Mar 2026 - 12:28

score 161 · Answer 11 · 2026-03-26 11:04:58

161

Views

Is $A_4 \times \mathbb{Z}_3$ isomorphic to $S_3 \times S_3$?

Published on 26 Mar 2026 - 11:04

score 396 · Answer 12 · 2026-03-27 12:28:59

396

Views

The number of solutions to $x^k = a$ over $G$ a finite cyclic group is $\gcd(k,|G|)$

Published on 27 Mar 2026 - 12:28

score 43 · Answer 13 · 2026-03-25 04:41:05

43

Views

Exponent of $1+J(GF),$ $J$ stands for Jacobson radical.

Published on 25 Mar 2026 - 4:41

score 65 · Answer 14 · 2019-01-18 19:50:58

65

Views

About the order of a group element

Published on 18 Jan 2019 - 19:50

score 89 · Answer 15 · 2026-03-27 04:38:13

89

Views

Order of elements from coset and Schur-Zassenhaus Theorem (Exercise $3.B.6$ FGT)

Published on 27 Mar 2026 - 4:38

List Question

A permutation in $S_n$ whose cycle decomposition contains a transposition

Which of these numbers could be the exact number of elements of order $21$ in a group?

When is a group homomorphism “extendable”?

Let $p,q$ be odd primes. Prove that a group of order $2 pq$ is solvable.

Group generated by $(1234567)$ and $(26)(34)$ is of order 168.

Let $G$ be finite and every nonidentity element have prime order. If $Z(G)\neq\{e\}$, prove that every nonidentity element of $G$ has the same order.

Computing the class-preserving automorphism group of finite $p$-groups

Number of automorphisms on alternating group $A_n$.

Conjugacy classes in special linear groups over $\mathbb{Z}/p^k$

Prove that a finite Abelian group $G$ is not cyclic if and only if it contains a subgroup isomorphic to $\mathbb{Z}_p\times\mathbb{Z}_p$

Is $A_4 \times \mathbb{Z}_3$ isomorphic to $S_3 \times S_3$?

The number of solutions to $x^k = a$ over $G$ a finite cyclic group is $\gcd(k,|G|)$

Exponent of $1+J(GF),$ $J$ stands for Jacobson radical.

About the order of a group element

Order of elements from coset and Schur-Zassenhaus Theorem (Exercise $3.B.6$ FGT)

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