List questions from sylow-theory

Published on 21 Mar 2017 - 14:39

47

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Why does p divide [G:H] in the proof of the first Sylow thm?

Published on 24 Mar 2017 - 6:28

2.9k

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Classify all groups of order 66, up to isomorphism

Published on 25 Mar 2026 - 4:39

127

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Exercise on Sylow's theorems

Published on 31 Mar 2017 - 18:07

175

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$H$ contains a Sylow $p$-subgroup of $G$ if and only if |$G$:$H$| is coprime to $p$.

Published on 06 Apr 2017 - 15:16

1.7k

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If $K$ is a normal subgroup of $N$, prove that $K$ is normal in $G$.

Published on 07 Apr 2017 - 3:44

1.2k

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List the Sylow 2-subgroups and Sylow 3-subgrousp of $U_{45}$

Published on 07 Apr 2017 - 4:18

54

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If $n=m.p^a$ where $p$ Is a prime and $p$ does not divide m

Published on 07 Apr 2017 - 5:14

195

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If $K$ is a Sylow p-subgroup of $G$ and $H$ is not normal in G, is $H\cap K$ a Sylow p-subgroup of $H$?

Published on 08 Apr 2017 - 0:45

293

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Must a group of order $20$ have an element of order $10$?

Published on 03 Feb 2023 - 14:34

348

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A group is solvable if it has only one $p$-Sylow subgroup for each $p$

Published on 26 Mar 2026 - 17:33

155

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I. M. Isaacs Algebra Exercise 9.4

Published on 23 Feb 2023 - 14:47

79

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Group Homology of a Sylow $p$-Subgroup

Published on 25 Mar 2026 - 23:52

230

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Prove every Sylow Subgroup of $G$ is Cyclic

Published on 21 Mar 2023 - 1:20

134

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Determination of the Groups of Order $99$

Published on 02 Apr 2023 - 17:18

List Question

Group of order 30 sylow-subgroups

Why does p divide [G:H] in the proof of the first Sylow thm?

Classify all groups of order 66, up to isomorphism

Exercise on Sylow's theorems

$H$ contains a Sylow $p$-subgroup of $G$ if and only if |$G$:$H$| is coprime to $p$.

If $K$ is a normal subgroup of $N$, prove that $K$ is normal in $G$.

List the Sylow 2-subgroups and Sylow 3-subgrousp of $U_{45}$

If $n=m.p^a$ where $p$ Is a prime and $p$ does not divide m

If $K$ is a Sylow p-subgroup of $G$ and $H$ is not normal in G, is $H\cap K$ a Sylow p-subgroup of $H$?

Must a group of order $20$ have an element of order $10$?

A group is solvable if it has only one $p$-Sylow subgroup for each $p$

I. M. Isaacs Algebra Exercise 9.4

Group Homology of a Sylow $p$-Subgroup

Prove every Sylow Subgroup of $G$ is Cyclic

Determination of the Groups of Order $99$

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