List questions from finite-groups

Published on 26 Mar 2026 - 12:53

6.8k

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Prove that if $H$ is a subgroup of index $2$ in a finite group $G$, then $gH=Hg$ for all $g\in G$

Published on 27 Mar 2026 - 23:35

41

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Finite groups and one-to-one functions on them.

Published on 17 Mar 2014 - 20:46

161

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Subgroups of a finite abelian group

Published on 27 Mar 2026 - 19:32

416

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Using the conjugacy class equation

Published on 27 Mar 2026 - 17:50

969

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Does every finite nilpotent group occur as a Frattini subgroup?

Published on 19 Mar 2014 - 1:40

577

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Normalizer of a Sylow subgroup

Published on 27 Mar 2026 - 14:10

100

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When would a finite group be considered as Fp G -Module?

Published on 19 Mar 2014 - 20:08

46

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What are all of the possible orders of $K$? Justify your answer.

Published on 19 Mar 2014 - 22:54

1.2k

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Prove that $G$ is the internal direct product of their normal subgroups $N_1,N_2,\ldots ,N_n$?

Published on 20 Mar 2014 - 4:42

154

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Unique intermediate subgroup and double coset relation I

Published on 21 Mar 2014 - 0:05

73

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Find all the groups $G$ such that $|G|\leq 6$

Published on 21 Mar 2014 - 4:16

123

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irreducible polynomial of $\alpha$ over $\mathbb{Q}$

Published on 27 Mar 2026 - 15:07

923

Views

Prove $G$ has a normal Sylow subgroup

Published on 26 Mar 2026 - 9:49

645

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Show that the p-Sylow subgroup is normal in $G$

Published on 26 Mar 2026 - 12:58

List Question

Finite group $G$ is product of a subgroup $H$ and normalizer of a Sylow $p$-subgroup of $H$

Prove that if $H$ is a subgroup of index $2$ in a finite group $G$, then $gH=Hg$ for all $g\in G$

Finite groups and one-to-one functions on them.

Subgroups of a finite abelian group

Using the conjugacy class equation

Does every finite nilpotent group occur as a Frattini subgroup?

Normalizer of a Sylow subgroup

When would a finite group be considered as Fp G -Module?

What are all of the possible orders of $K$? Justify your answer.

Prove that $G$ is the internal direct product of their normal subgroups $N_1,N_2,\ldots ,N_n$?

Unique intermediate subgroup and double coset relation I

Find all the groups $G$ such that $|G|\leq 6$

irreducible polynomial of $\alpha$ over $\mathbb{Q}$

Prove $G$ has a normal Sylow subgroup

Show that the p-Sylow subgroup is normal in $G$

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