List questions from finite-groups

Published on 26 Mar 2026 - 3:01

564

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Group of order $pqr$

Published on 26 Mar 2026 - 4:32

93

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Maximal subgroup of Wreathed 2-groups

Published on 25 Mar 2026 - 9:26

240

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Can any finite group of order $n$ be embedded in $SL_n(\mathbb{Z})$?

Published on 22 Mar 2026 - 12:03

294

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Proving $\left(\mathbb{Z}/p^{d} \mathbb{Z}\right)^{\times}$ is cyclic for prime p

Published on 04 Feb 2019 - 22:08

378

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Cauchy's theorem proof clarification (group theory)

Published on 25 Mar 2026 - 7:41

68

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For which $n\in \Bbb N$ is $H_n:=\{\alpha^2\mid \alpha\in S_n\}\cong A_n?$

Published on 26 Mar 2026 - 12:48

464

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Is every group of order 117 abelian?

Published on 06 Feb 2019 - 12:51

105

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For $n>1$, let $H$ be the set of all products in $S_n$ of a multiple of four transpositions. Show $H=A_n$.

Published on 26 Mar 2026 - 12:50

77

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If $G = H \cup K \cup L$, then $[G:H] = [G:K] = [G:L]=2$

Published on 07 Feb 2019 - 18:59

153

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How do I turn a group presentation into a multiplication table?

Published on 25 Mar 2026 - 9:23

379

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Is a finite centerless metabelian group always a semidirect product of two abelian groups?

Published on 22 Mar 2026 - 9:03

47

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Suppose $G$ is a group of order $n$ . Let $p$ and $q$ be distinct primes which divide $n$. Can we say that $G$ has a subgroup of order $p\cdot q$?

Published on 09 Feb 2019 - 16:29

167

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Question about commutativity of conjugacy classes

Published on 09 Feb 2019 - 17:03

106

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Is the normality of a subgroup dependent on which group is its parent?

Published on 27 Mar 2026 - 12:14

List Question

Property of Sylow $2$-subgroups of $S_n$ and $S_{n+1}$

Group of order $pqr$

Maximal subgroup of Wreathed 2-groups

Can any finite group of order $n$ be embedded in $SL_n(\mathbb{Z})$?

Proving $\left(\mathbb{Z}/p^{d} \mathbb{Z}\right)^{\times}$ is cyclic for prime p

Cauchy's theorem proof clarification (group theory)

For which $n\in \Bbb N$ is $H_n:=\{\alpha^2\mid \alpha\in S_n\}\cong A_n?$

Is every group of order 117 abelian?

For $n>1$, let $H$ be the set of all products in $S_n$ of a multiple of four transpositions. Show $H=A_n$.

If $G = H \cup K \cup L$, then $[G:H] = [G:K] = [G:L]=2$

How do I turn a group presentation into a multiplication table?

Is a finite centerless metabelian group always a semidirect product of two abelian groups?

Suppose $G$ is a group of order $n$ . Let $p$ and $q$ be distinct primes which divide $n$. Can we say that $G$ has a subgroup of order $p\cdot q$?

Question about commutativity of conjugacy classes

Is the normality of a subgroup dependent on which group is its parent?

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