List questions from finite-groups

Published on 08 Sep 2014 - 21:49

234

Views

How to show that the normalizer N of a Sylow $p$-subgroup P of $S_p$ in $S_p$ is the affine linear group AGL(1,$p$)?

Published on 28 Mar 2026 - 15:21

3.8k

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Is there a simple group of order $105$?

Published on 09 Sep 2014 - 4:49

804

Views

If $G$ is a finite group whose $p$-Sylow subgroup $P$ lies in its center, then there is a normal subgroup $N$ of $G$ with $P\cap N=\{e\}$ and $PN=G$

Published on 26 Mar 2026 - 23:10

60

Views

Let $ G$ be a nilpotent group. prove that there exist $a\in G$, such that $ o(a)=exp(G)$.

Published on 09 Sep 2014 - 9:28

108

Views

non-abelian simple group

Published on 09 Sep 2014 - 10:34

225

Views

Direct product of two groups.

Published on 09 Sep 2014 - 11:01

313

Views

Hecke Operators

Published on 28 Mar 2026 - 1:26

313

Views

question on nilpotent group.

Published on 05 Apr 2026 - 20:13

289

Views

Rapid question on minimal normal subgroups

Published on 10 Sep 2014 - 19:03

66

Views

Normal subgroup of a finite group

Published on 28 Mar 2026 - 15:26

148

Views

Connections of Finite groups and quantum groups

Published on 27 Mar 2026 - 10:04

83

Views

An equality from Representation Theory

Published on 12 Sep 2014 - 17:55

173

Views

Field that contains $(\mathbb{Z}/p^n\mathbb{Z})^*$

Published on 13 Sep 2014 - 15:00

3.5k

Views

Group of order $pq$ with $p\not\mid (q-1)$

Published on 29 Mar 2026 - 19:10

List Question

prove that the no of normal subgroups of a fixed order containing K is congruent to 1 mod p.

How to show that the normalizer N of a Sylow $p$-subgroup P of $S_p$ in $S_p$ is the affine linear group AGL(1,$p$)?

Is there a simple group of order $105$?

If $G$ is a finite group whose $p$-Sylow subgroup $P$ lies in its center, then there is a normal subgroup $N$ of $G$ with $P\cap N=\{e\}$ and $PN=G$

Let $ G$ be a nilpotent group. prove that there exist $a\in G$, such that $ o(a)=exp(G)$.

non-abelian simple group

Direct product of two groups.

Hecke Operators

question on nilpotent group.

Rapid question on minimal normal subgroups

Normal subgroup of a finite group

Connections of Finite groups and quantum groups

An equality from Representation Theory

Field that contains $(\mathbb{Z}/p^n\mathbb{Z})^*$

Group of order $pq$ with $p\not\mid (q-1)$

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