List questions from finite-groups

Published on 25 Mar 2026 - 12:24

45

Views

An upper bound for the number of semidirect products of a finite group up to isomorphism

Published on 25 Mar 2026 - 4:43

79

Views

$|G|= 2^n, o(g)=2~\forall g \in G, g \neq e$ show that G is abelian

Published on 12 May 2018 - 13:30

804

Views

GCD and the cycle decomposition of a permutation

Published on 25 Mar 2026 - 14:31

256

Views

Proving a binary operation is not associative given a latin square

Published on 20 Mar 2026 - 1:03

175

Views

Isomorphic subgroups of $S_n$ and bijection of sets

Published on 13 May 2018 - 6:09

570

Views

Proving a finite group is isomorphic to $(\Bbb Z/2)^n$

Published on 13 May 2018 - 7:03

112

Views

Invariants of $\mathbb{Z}[x, x^{-1}, y, y^{-1}]$ under actions of finite subgroups in $\text{GL}(2, \mathbb{Z})$

Published on 26 Mar 2026 - 7:57

69

Views

Appeal for clarification of an isomorphism between $\operatorname{Aut}_c(G)$ and $\operatorname{Hom}(G,Z(G))$

Published on 25 Mar 2026 - 9:29

50

Views

If $G$ is a finite $p$-group with $Z(G) = [G,G]$, then $\exp(G/Z(G)) = \exp(Z(G))$.

Published on 14 May 2018 - 17:34

252

Views

Parallel lines over finite fields

Published on 26 Mar 2026 - 6:18

1.1k

Views

How to find the number of elements with a particular order in a cyclic group?

Published on 26 Mar 2026 - 2:45

61

Views

The sum of the values of the character of a given group representation

Published on 25 Mar 2026 - 1:20

993

Views

The radical and socle series of a module and its dual

Published on 22 Mar 2026 - 17:08

56

Views

Is the subgroup order always a multiple of it's generators order?

Published on 25 Mar 2026 - 7:55

List Question

Centralizers in the Symmetric Group

An upper bound for the number of semidirect products of a finite group up to isomorphism

$|G|= 2^n, o(g)=2~\forall g \in G, g \neq e$ show that G is abelian

GCD and the cycle decomposition of a permutation

Proving a binary operation is not associative given a latin square

Isomorphic subgroups of $S_n$ and bijection of sets

Proving a finite group is isomorphic to $(\Bbb Z/2)^n$

Invariants of $\mathbb{Z}[x, x^{-1}, y, y^{-1}]$ under actions of finite subgroups in $\text{GL}(2, \mathbb{Z})$

Appeal for clarification of an isomorphism between $\operatorname{Aut}_c(G)$ and $\operatorname{Hom}(G,Z(G))$

If $G$ is a finite $p$-group with $Z(G) = [G,G]$, then $\exp(G/Z(G)) = \exp(Z(G))$.

Parallel lines over finite fields

How to find the number of elements with a particular order in a cyclic group?

The sum of the values of the character of a given group representation

The radical and socle series of a module and its dual

Is the subgroup order always a multiple of it's generators order?

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