List questions from finite-groups

Published on 10 Apr 2026 - 4:26

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Group $G$ cyclic as it coincides with the multiplicative group of a finite field

Published on 14 Apr 2026 - 2:48

82

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Permutation Product

Published on 09 Apr 2026 - 18:47

41

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Different Representation Matrices from same Generating Set

Published on 25 Mar 2026 - 6:26

98

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Need help in understanding the example from Dummit & Foote text

Published on 08 Apr 2026 - 21:58

624

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Cyclic permutation group example ($n>1$)

Published on 17 Apr 2026 - 18:01

372

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If $H<G$ is abelian, and $\chi(1)=[G:H]$ for irreducible $\chi$, then $H$ contains a nontrivial normal subgroup?

Published on 14 Apr 2026 - 4:26

1.9k

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If $H$ is a subgroup of $G$ of index $n$, then $g^{n!} \in H \ \forall g \in G$

Published on 16 Apr 2026 - 4:28

148

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Upper-bounding a sum over non-identity permutations

Published on 11 Apr 2026 - 18:47

83

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A normal subgroup $N$ of $G$ with $\operatorname{gcd}(|N|,|G/N|)=1$

Published on 17 Apr 2026 - 1:06

424

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Number of subgroups of groups with prime power order

Published on 14 Apr 2026 - 22:26

85

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Group $G$ with $ord(G)=319$ is a cyclic group

Published on 14 Apr 2026 - 22:01

113

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How to write $\Bbb Z_q\rtimes\Bbb Z_p$ as $\langle a,b\mid a^p=b^q=1,aba^{-1}=b^{i_0}\rangle?$

Published on 26 Mar 2026 - 4:14

1.1k

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Books on Group Theory.

Published on 10 Apr 2026 - 23:04

225

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Cohomology ring of $G$ based on its Sylow.

Published on 12 Apr 2026 - 1:11

List Question

Does Abelianization Commute with Profinite Completion?

Group $G$ cyclic as it coincides with the multiplicative group of a finite field

Permutation Product

Different Representation Matrices from same Generating Set

Need help in understanding the example from Dummit & Foote text

Cyclic permutation group example ($n>1$)

If $H<G$ is abelian, and $\chi(1)=[G:H]$ for irreducible $\chi$, then $H$ contains a nontrivial normal subgroup?

If $H$ is a subgroup of $G$ of index $n$, then $g^{n!} \in H \ \forall g \in G$

Upper-bounding a sum over non-identity permutations

A normal subgroup $N$ of $G$ with $\operatorname{gcd}(|N|,|G/N|)=1$

Number of subgroups of groups with prime power order

Group $G$ with $ord(G)=319$ is a cyclic group

How to write $\Bbb Z_q\rtimes\Bbb Z_p$ as $\langle a,b\mid a^p=b^q=1,aba^{-1}=b^{i_0}\rangle?$

Books on Group Theory.

Cohomology ring of $G$ based on its Sylow.

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