List questions from sylow-theory

Published on 08 Sep 2014 - 12:48

803

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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 09 Sep 2014 - 5:28

253

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Number of Sylow 2-subgroups of a special linear group

Published on 12 Sep 2014 - 6:04

3.8k

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A p subgroup of a group is contained in a sylow p subgroup

Published on 13 Sep 2014 - 11:18

100

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Prove that the normaliser of a Sylow $2$-subgroups of $D_{2n}$ is itself.

Published on 14 Sep 2014 - 22:16

1.8k

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A group $G$ with $|G|=p^3q$ and with no normal Sylow subgroups is $G \cong \mathbb S_4$

Published on 15 Sep 2014 - 13:31

303

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Find all Sylow 3-subgroups of $S_3\times S_3$

Published on 16 Sep 2014 - 16:53

197

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Sylow subgroups problem

Published on 17 Sep 2014 - 3:20

958

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There are no simple groups of order $27p$

Published on 25 Mar 2026 - 11:11

746

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Sylow subgroups of a non abelian group $G$ with $|G|=21$ and $|G|=39$

Published on 19 Sep 2014 - 19:35

5.2k

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Group of order $|G|=pqr$, $p,q,r$ primes has a normal subgroup of order

Published on 21 Sep 2014 - 15:13

1.1k

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Prove that $n_p(N)$ divides $n_p(G)$

Published on 21 Sep 2014 - 17:20

237

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If $G$ is a group of order $48$, show that the intersection of any two distinct Sylow $2$-subgroups has order $8$

Published on 23 Sep 2014 - 17:12

156

Views

Lang Sylow Theorem

Published on 01 Oct 2014 - 19:05

689

Views

Hall's Subgroup Theorem

Published on 25 Mar 2026 - 17:44

List Question

Sylow Subgroup is

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 $PN=G$

Number of Sylow 2-subgroups of a special linear group

A p subgroup of a group is contained in a sylow p subgroup

Prove that the normaliser of a Sylow $2$-subgroups of $D_{2n}$ is itself.

A group $G$ with $|G|=p^3q$ and with no normal Sylow subgroups is $G \cong \mathbb S_4$

Find all Sylow 3-subgroups of $S_3\times S_3$

Sylow subgroups problem

There are no simple groups of order $27p$

Sylow subgroups of a non abelian group $G$ with $|G|=21$ and $|G|=39$

Group of order $|G|=pqr$, $p,q,r$ primes has a normal subgroup of order

Prove that $n_p(N)$ divides $n_p(G)$

If $G$ is a group of order $48$, show that the intersection of any two distinct Sylow $2$-subgroups has order $8$

Lang Sylow Theorem

Hall's Subgroup Theorem

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