List questions from finite-groups

Published on 13 Nov 2014 - 18:22

506

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Is $ G \cong G/N \times N$?

Published on 13 Nov 2014 - 21:58

534

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$S$ nonempty finite subset of group $G$ for which $SS=S$. $S$ is subgroup.

Published on 29 Mar 2026 - 18:07

113

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if $k$ is a positive integer and $G$ a finite group such that $G=\{x^k:x\in G\}$ , then is it true that g.c.d.$(|G|,k)=1$ ?

Published on 15 Nov 2014 - 14:20

134

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Why is $G$ abelian?

Published on 27 Mar 2026 - 6:51

309

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proof of a useful counting result in group theory

Published on 28 Mar 2026 - 23:58

486

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Given a representation $\rho$ of a finite group, why is $\rho(g)$ always diagonalisable?

Published on 16 Nov 2014 - 11:04

1.8k

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Any group which is of prime order is a cyclic group

Published on 16 Nov 2014 - 11:31

75

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Character of the algebra $\mathbb{C}[G]$ as $G \times G $-module

Published on 26 Mar 2026 - 1:14

8.6k

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Question about Z12≃Z4⊕Z3 generators and order

Published on 29 Mar 2026 - 10:37

609

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Sylow $p$-subgroup of $GL_{n}(\mathbb{F}_{q})$

Published on 27 Mar 2026 - 6:56

151

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showing that $G$ is not solvable.

Published on 16 Nov 2014 - 23:26

156

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showing that $G$ is nilpotent.

Published on 17 Nov 2014 - 0:23

45

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How do I know the cyclic subgroups of G generated by a are equal?

Published on 29 Mar 2026 - 10:37

45

Views

Getting the least possible order of a group from existing cyclic subgroups or elements.

Published on 29 Mar 2026 - 10:37

List Question

Automorphism Tower for $\Bbb Z_4$, $\Bbb Z_3$, $\Bbb Z_2 \times \Bbb Z_2$

Is $ G \cong G/N \times N$?

$S$ nonempty finite subset of group $G$ for which $SS=S$. $S$ is subgroup.

if $k$ is a positive integer and $G$ a finite group such that $G=\{x^k:x\in G\}$ , then is it true that g.c.d.$(|G|,k)=1$ ?

Why is $G$ abelian?

proof of a useful counting result in group theory

Given a representation $\rho$ of a finite group, why is $\rho(g)$ always diagonalisable?

Any group which is of prime order is a cyclic group

Character of the algebra $\mathbb{C}[G]$ as $G \times G $-module

Question about Z12≃Z4⊕Z3 generators and order

Sylow $p$-subgroup of $GL_{n}(\mathbb{F}_{q})$

showing that $G$ is not solvable.

showing that $G$ is nilpotent.

How do I know the cyclic subgroups of G generated by a are equal?

Getting the least possible order of a group from existing cyclic subgroups or elements.

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