List questions from sylow-theory

Published on 26 Mar 2026 - 14:42

95

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If $|G|=pqr$ show that $G\cong P\times QR$ where $P,Q,R$ are sylow-$p,q,r$ subgroups respectively under certain conditions

Published on 26 Mar 2026 - 19:20

1.7k

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Let $H$ be a normal $p$ -subgroup of a finite group $G$ ,then $H$ is contained into each Sylow $p$ subgroup of $G$

Published on 18 Feb 2017 - 10:04

380

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A group of order $595$ has a normal subgroup of order $17$

Published on 18 Feb 2017 - 13:34

525

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The size of normalizer of intersection of two distinct Sylow $p$-subgroups

Published on 24 Feb 2017 - 5:59

2.3k

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Is a group of order 225 an abelian group?

Published on 03 Mar 2017 - 15:49

651

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Proof of existence of Sylow p-subgroup

Published on 04 Mar 2017 - 10:56

336

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Show that there exists a Sylow p-group P of G such that $P_1 = P\cap H$.

Published on 08 Mar 2017 - 8:53

2.1k

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$G$ group of order $36$, $H\le G$ of order $9$. Show that either $H\unlhd G$ or there is $K\le H$ of order $3$, $K\unlhd G$.

Published on 11 Mar 2017 - 16:57

196

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Number of $p$-groups of a given size in a Sylow subgroup

Published on 26 Mar 2026 - 3:12

122

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Proof of first Sylow theorem concerning conjugation of two coset/two orbits of length 1

Published on 12 Mar 2017 - 13:09

1.2k

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Sylow theorems exercise

Published on 12 Mar 2017 - 20:18

139

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Group of order $3^k5^l$ is solvable

Published on 26 Mar 2026 - 3:11

1.6k

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How do we know all Sylow $p$-subgroups of a given order are distinct?

Published on 26 Mar 2026 - 6:28

3k

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How many subgroups of order 17 does $S_{17}$ have?

Published on 19 Mar 2017 - 14:34

List Question

Is a group of order 1280 simple or not?

If $|G|=pqr$ show that $G\cong P\times QR$ where $P,Q,R$ are sylow-$p,q,r$ subgroups respectively under certain conditions

Let $H$ be a normal $p$ -subgroup of a finite group $G$ ,then $H$ is contained into each Sylow $p$ subgroup of $G$

A group of order $595$ has a normal subgroup of order $17$

The size of normalizer of intersection of two distinct Sylow $p$-subgroups

Is a group of order 225 an abelian group?

Proof of existence of Sylow p-subgroup

Show that there exists a Sylow p-group P of G such that $P_1 = P\cap H$.

$G$ group of order $36$, $H\le G$ of order $9$. Show that either $H\unlhd G$ or there is $K\le H$ of order $3$, $K\unlhd G$.

Number of $p$-groups of a given size in a Sylow subgroup

Proof of first Sylow theorem concerning conjugation of two coset/two orbits of length 1

Sylow theorems exercise

Group of order $3^k5^l$ is solvable

How do we know all Sylow $p$-subgroups of a given order are distinct?

How many subgroups of order 17 does $S_{17}$ have?

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