List questions from finite-groups

Published on 14 May 2014 - 5:47

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A finite $p$-group has normal subgroup of index $p^2$

Published on 14 May 2014 - 8:59

92

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Finding Sylow p subgroups and determining group structure using Sylow's Theorem.

Published on 14 May 2014 - 13:19

41

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Counting homomorphisms by the order of their images

Published on 28 Mar 2026 - 5:22

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nilpotent group implies solvable group

Published on 25 Mar 2026 - 9:32

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Let $G$ be a finite simple group. Suppose that $H$ is a subgroup of $G$ with index $n=|G:H|>1$. Show that $|H|$ divides $(n-1)!$

Published on 25 Mar 2026 - 9:50

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This is about Sylow subgroups of Alternating group $A_n$ (Multiple choice)

Published on 26 Mar 2026 - 17:52

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$|G|=p^3$ non abelian $\Longrightarrow\gamma_2(G)\lneq Z(G)$

Published on 25 Mar 2026 - 16:03

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Cayley's theorem : precision

Published on 26 Mar 2026 - 6:26

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A Group of Order $540$ is not simple

Published on 26 Mar 2026 - 17:52

47

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Can we have this sort of a representation in a finite group?

Published on 17 May 2014 - 10:13

116

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Is this a proof by contradiction?

Published on 28 Mar 2026 - 6:59

728

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Cauchy's Theorem $\#$ of elements order $p$

Published on 25 Mar 2026 - 17:36

108

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Does this set can say more about group?

Published on 18 May 2014 - 0:00

83

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What are all possible automorphisms of the Klein's 4-group?

Published on 18 May 2014 - 6:54

List Question

A finite group containing an element with some property is a $p$-group

A finite $p$-group has normal subgroup of index $p^2$

Finding Sylow p subgroups and determining group structure using Sylow's Theorem.

Counting homomorphisms by the order of their images

nilpotent group implies solvable group

Let $G$ be a finite simple group. Suppose that $H$ is a subgroup of $G$ with index $n=|G:H|>1$. Show that $|H|$ divides $(n-1)!$

This is about Sylow subgroups of Alternating group $A_n$ (Multiple choice)

$|G|=p^3$ non abelian $\Longrightarrow\gamma_2(G)\lneq Z(G)$

Cayley's theorem : precision

A Group of Order $540$ is not simple

Can we have this sort of a representation in a finite group?

Is this a proof by contradiction?

Cauchy's Theorem $\#$ of elements order $p$

Does this set can say more about group?

What are all possible automorphisms of the Klein's 4-group?

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