List questions from sylow-theory

Published on 19 Apr 2014 - 23:26

245

Views

Show that $N_G(H) = H$

Published on 21 Apr 2014 - 16:48

721

Views

Show that if the prime $p$ divides $|G|$, then $|X|$ is divisible by $p$.

Published on 22 Apr 2014 - 2:56

77

Views

Ruling out orders when applying Sylow's theorems

Published on 23 Apr 2014 - 3:49

794

Views

Finding the number of Sylow p-subgroups

Published on 25 Apr 2014 - 17:21

120

Views

Is there a general method of finding the number of Sylow p-subgroups, given only the order of the group?

Published on 26 Apr 2014 - 14:38

583

Views

Sylow $7$-subgroup of a group of order $4\cdot3\cdot5\cdot7$ is normal

Published on 29 Apr 2014 - 6:25

703

Views

A question about the involution in simple groups.

Published on 25 Mar 2026 - 8:05

118

Views

Let $K$ be a subgroup of $H$ of order 5. Prove that $N(K)\ge N(H)$

Published on 06 May 2014 - 21:11

420

Views

Question about a non-abelian group of order $p^2q$

Published on 07 May 2014 - 15:07

1.6k

Views

What do Sylow 2-subgroups of finite simple groups look like?

Published on 21 Mar 2026 - 11:53

3.4k

Views

showing that a group of order 45 is abelian

Published on 12 May 2014 - 8:06

72

Views

question about $p$-Sylow subgroups

Published on 13 May 2014 - 16:54

138

Views

Fixed Points and Sylow-Subgroups of Subgroups who are also Sylow-Subgroups of whole Group

Published on 13 May 2014 - 21:53

393

Views

if $Q$ and $P$ are distinct $p$-Sylow subgroups then $Q\not\subseteq N_G(P)$.

Published on 14 May 2014 - 10:02

List Question

Sylow p-subgroup: Understanding a proof

Show that $N_G(H) = H$

Show that if the prime $p$ divides $|G|$, then $|X|$ is divisible by $p$.

Ruling out orders when applying Sylow's theorems

Finding the number of Sylow p-subgroups

Is there a general method of finding the number of Sylow p-subgroups, given only the order of the group?

Sylow $7$-subgroup of a group of order $4\cdot3\cdot5\cdot7$ is normal

A question about the involution in simple groups.

Let $K$ be a subgroup of $H$ of order 5. Prove that $N(K)\ge N(H)$

Question about a non-abelian group of order $p^2q$

What do Sylow 2-subgroups of finite simple groups look like?

showing that a group of order 45 is abelian

question about $p$-Sylow subgroups

Fixed Points and Sylow-Subgroups of Subgroups who are also Sylow-Subgroups of whole Group

if $Q$ and $P$ are distinct $p$-Sylow subgroups then $Q\not\subseteq N_G(P)$.

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