List questions from finite-groups

Published on 27 Mar 2026 - 14:59

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Commutator subgroup of $G=\langle a,b,c,d:a^4=b^2=c^2=d^q=1,ab=ba,ac=ca,bc=cb,d^{-1}ad=b,d^{-1}bd=c,d^{-1}cd=ab \rangle$

Published on 25 Mar 2026 - 22:05

1.9k

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How do I find all the subgroups of the symmetry group of an equilateral triangle?

Published on 26 Mar 2026 - 11:01

70

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Isomorphism between two finite order groups

Published on 15 Oct 2019 - 2:59

50

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For each of the following numbers $n$, decide whether or not $O(G)$ must contain $n$?

Published on 15 Oct 2019 - 16:39

107

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Minimal possible order of a group that contains a specific subset

Published on 15 Oct 2019 - 19:18

1.5k

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Let $H$ and $K$ be subgroups of a finite cyclic group $G.$ Prove $|H \cap K| = \gcd(|H|,|K|)$

Published on 29 Mar 2026 - 15:33

55

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Polynomial invariants of finite groups preserved under epimorphism

Published on 25 Mar 2026 - 22:04

106

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$G$ is a finite group and $H \subseteq G$ such that $\forall a,b \in H: ab\in H$. Prove that $H\le G$.

Published on 16 Oct 2019 - 13:16

34

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A question about "commuting graph universality"?

Published on 16 Oct 2019 - 13:33

131

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Is any braid group generated by finite "transpositions"?

Published on 02 Apr 2026 - 17:01

555

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How to show that a group of order $380$ always has a normal subgroup of $95$

Published on 27 Mar 2026 - 11:49

109

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Showing $12\Bbb Z<\Bbb Z$ as groups.

Published on 17 Oct 2019 - 18:17

48

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Presentation of $Q_{4n}$, $n \in \mathbb{N}$

Published on 26 Mar 2026 - 1:03

183

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Why doesn't every group have order $2^n$?

Published on 29 Mar 2026 - 21:51

List Question

Prove that $S_3$ and a subgroup $H$ of $S_4$ are isomorphic.

Commutator subgroup of $G=\langle a,b,c,d:a^4=b^2=c^2=d^q=1,ab=ba,ac=ca,bc=cb,d^{-1}ad=b,d^{-1}bd=c,d^{-1}cd=ab \rangle$

How do I find all the subgroups of the symmetry group of an equilateral triangle?

Isomorphism between two finite order groups

For each of the following numbers $n$, decide whether or not $O(G)$ must contain $n$?

Minimal possible order of a group that contains a specific subset

Let $H$ and $K$ be subgroups of a finite cyclic group $G.$ Prove $|H \cap K| = \gcd(|H|,|K|)$

Polynomial invariants of finite groups preserved under epimorphism

$G$ is a finite group and $H \subseteq G$ such that $\forall a,b \in H: ab\in H$. Prove that $H\le G$.

A question about "commuting graph universality"?

Is any braid group generated by finite "transpositions"?

How to show that a group of order $380$ always has a normal subgroup of $95$

Showing $12\Bbb Z<\Bbb Z$ as groups.

Presentation of $Q_{4n}$, $n \in \mathbb{N}$

Why doesn't every group have order $2^n$?

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