List questions from sylow-theory

Published on 15 May 2014 - 10:07

121

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Does Sylow's theorem assert the existence of subgroups of order $p^j$ for all $j=1,\dots,k$ ?

Published on 15 May 2014 - 15:12

58

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Proving group is $p$-group by contradiction

Published on 25 Mar 2026 - 17:37

1.7k

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A Group of Order $540$ is not simple

Published on 16 May 2014 - 20:40

574

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How many nonabelian groups of order 2009? (Check work)

Published on 25 Mar 2026 - 7:48

463

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Question about Sylow $p$-subgroups

Published on 27 May 2014 - 3:16

677

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trouble applying Sylow's theorems

Published on 28 May 2014 - 22:48

469

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If Q is a p-Sylow-Group of H there is a p-Sylow-Group P of G with $\phi(P)=Q$ while $\phi:G\rightarrow H$ epimorphism

Published on 29 May 2014 - 16:28

395

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Sylow questions on $GL_2(\mathbb F_3)$.

Published on 29 May 2014 - 18:24

1.5k

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Question about $p$-Sylow subgroups of the quotient group

Published on 30 May 2014 - 0:01

87

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Let $F$ be a free centralizer in $G$. Then $F=P\times A$, where $P$ is a Sylow $p$-subgroup of $F$ and $A$ is abelian.

Published on 30 May 2014 - 11:55

95

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$P\in Syl_p(G)\Rightarrow|G:N_G(P)|=|Syl_p(G)|$

Published on 30 May 2014 - 15:27

4.2k

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Subgroups of a group of order 60 with a normal subgroup of order 2 (Sylow)

Published on 02 Jun 2014 - 21:53

7.7k

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How many normal subgroups does a non-abelian group $G$ of order $ 21$ have?

Published on 03 Jun 2014 - 12:25

248

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Question about Sylow Theorem and normalizer

Published on 04 Jun 2014 - 19:50

List Question

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

Does Sylow's theorem assert the existence of subgroups of order $p^j$ for all $j=1,\dots,k$ ?

Proving group is $p$-group by contradiction

A Group of Order $540$ is not simple

How many nonabelian groups of order 2009? (Check work)

Question about Sylow $p$-subgroups

trouble applying Sylow's theorems

If Q is a p-Sylow-Group of H there is a p-Sylow-Group P of G with $\phi(P)=Q$ while $\phi:G\rightarrow H$ epimorphism

Sylow questions on $GL_2(\mathbb F_3)$.

Question about $p$-Sylow subgroups of the quotient group

Let $F$ be a free centralizer in $G$. Then $F=P\times A$, where $P$ is a Sylow $p$-subgroup of $F$ and $A$ is abelian.

$P\in Syl_p(G)\Rightarrow|G:N_G(P)|=|Syl_p(G)|$

Subgroups of a group of order 60 with a normal subgroup of order 2 (Sylow)

How many normal subgroups does a non-abelian group $G$ of order $ 21$ have?

Question about Sylow Theorem and normalizer

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