User James

2 votes

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Reference enumerating groups of order a product of five distinct primes.

answered Dec 12, 2023 at 6:22

2 votes

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$n$ such that the number of groups of order $n$ up to isomorphism is $33$

answered Dec 10, 2023 at 5:49

2 votes

What are the counter examples books for Abstract algebra?

answered Sep 8, 2023 at 18:45

2 votes

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Proving that every group of order a power of a prime has an element of order $p$

answered Jul 10, 2023 at 2:47

3 votes

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GAP: How to find a (possibly non-minimal) transitive representation of a group?

answered Jun 8, 2023 at 1:17

5 votes

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Outer automorphisms of a holomorph

answered Nov 21, 2022 at 2:32

1 vote

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Why that element belongs to FC subgroup?

answered Feb 24, 2021 at 4:56

5 votes

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Semidirect product of point stabiliser and regular normal subgroup.

answered Apr 13, 2020 at 1:22

3 votes

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What is the minimal possible order of an $n$-universal group?

answered Dec 29, 2019 at 6:42

0 votes

Normal subgroup fixes every element of a set.

answered Nov 14, 2019 at 23:23

1 vote

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Solvable groups as iterated semidirect products of supersolvable groups

answered Sep 14, 2019 at 9:00

4 votes

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An infinite torsion group with element orders sensitive to subgroups

answered Aug 26, 2014 at 2:01

8 votes

What is the easiest way to generate $\mathrm{GL}(n,\mathbb Z)$?

answered Jan 11, 2012 at 22:35

2 votes

Identifying the group in GAP

answered Apr 13, 2019 at 11:04

6 votes

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Is the free product of residually finite groups always residually finite?

answered Mar 12, 2019 at 21:06

2 votes

What natural ways of partitioning a group $G$ are there?

answered Jan 25, 2019 at 23:29

1 vote

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Prove that $H$ is a subgroup of $G$ if $H$ is non-empty and $gh^{-1} \in H$ whenever $g,h \in H$

answered Sep 30, 2018 at 12:40

13 votes

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Does every finite non-trivial complete group have even order?

answered Sep 5, 2018 at 18:09

8 votes

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Is there a way to describe all finite groups $G$, such that $\operatorname{Aut}(G) = D_4$?

answered Sep 23, 2018 at 14:18

2 votes

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Solvable, non-nilpotent group with nilpotent commutator subgroup

answered Aug 12, 2018 at 13:50

2 votes

Example of two subgroups $H$ and $K$ of a non-abelian group $G$ such that $HK$ is not a subgroup of $G$?

answered Aug 4, 2018 at 1:13

1 vote

Conditions for cyclic quotient group

answered Aug 4, 2018 at 0:19

4 votes

Conditions for cyclic quotient group

answered Aug 3, 2018 at 22:56

1 vote

Groups with large centers

answered Mar 11, 2018 at 13:06

4 votes

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Finite index subgroups of surface groups

answered Feb 21, 2018 at 3:51

0 votes

Derived Subgroup Criteria

answered Feb 16, 2018 at 3:09

4 votes

Find the group given the presentation

answered Feb 15, 2018 at 23:43

2 votes

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Does $Ab(\pi_1(\Sigma_2)/N)=1$ imply $\pi_1(\Sigma_2)/N = 1$?

answered Feb 15, 2018 at 22:27

1 vote

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Frobenius complements are nilpotent

answered Dec 6, 2017 at 22:31

4 votes

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Second derived subgroup is unit, why G/Z(G) is abelian?

answered Dec 6, 2017 at 21:49

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188 Answers

Reference enumerating groups of order a product of five distinct primes.

$n$ such that the number of groups of order $n$ up to isomorphism is $33$

What are the counter examples books for Abstract algebra?

Proving that every group of order a power of a prime has an element of order $p$

GAP: How to find a (possibly non-minimal) transitive representation of a group?

Outer automorphisms of a holomorph

Why that element belongs to FC subgroup?

Semidirect product of point stabiliser and regular normal subgroup.

What is the minimal possible order of an $n$-universal group?

Normal subgroup fixes every element of a set.

Solvable groups as iterated semidirect products of supersolvable groups

An infinite torsion group with element orders sensitive to subgroups

What is the easiest way to generate $\mathrm{GL}(n,\mathbb Z)$?

Identifying the group in GAP

Is the free product of residually finite groups always residually finite?

What natural ways of partitioning a group $G$ are there?

Prove that $H$ is a subgroup of $G$ if $H$ is non-empty and $gh^{-1} \in H$ whenever $g,h \in H$

Does every finite non-trivial complete group have even order?

Is there a way to describe all finite groups $G$, such that $\operatorname{Aut}(G) = D_4$?

Solvable, non-nilpotent group with nilpotent commutator subgroup

Example of two subgroups $H$ and $K$ of a non-abelian group $G$ such that $HK$ is not a subgroup of $G$?

Conditions for cyclic quotient group

Conditions for cyclic quotient group

Groups with large centers

Finite index subgroups of surface groups

Derived Subgroup Criteria

Find the group given the presentation

Does $Ab(\pi_1(\Sigma_2)/N)=1$ imply $\pi_1(\Sigma_2)/N = 1$?

Frobenius complements are nilpotent

Second derived subgroup is unit, why G/Z(G) is abelian?