Question

Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group

score 3k · Answer 1 · 2014-08-08 22:45:17

3k

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Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group

Published on 08 Aug 2014 - 22:45

score 177 · Answer 2 · 2014-08-11 13:04:35

177

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Proof of Cauchy's Lemma in the case that G is abelian

Published on 11 Aug 2014 - 13:04

score 1.6k · Answer 3 · 2014-08-13 19:11:44

1.6k

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Let $G$ be finite, $H\unlhd G.$ Let $P$ be a Sylow $p$-subgroup of $H.$ Use Sylow's theorem to show $G = H N_G(P).$

Published on 13 Aug 2014 - 19:11

score 63 · Answer 4 · 2014-08-14 19:50:54

63

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Group with order $|G|=p^2q^2$ and $p\not\mid q-1, p\not\mid q+1$

Published on 14 Aug 2014 - 19:50

score 775 · Answer 5 · 2014-08-14 22:23:09

775

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Understanding what the Sylow theorems say about $p$-groups

Published on 14 Aug 2014 - 22:23

score 2.4k · Answer 6 · 2014-08-23 21:05:19

2.4k

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Let $G$ be a finite group and let $a$ be an element of $G$. Then, $|cl ~(a)| = |G:C(a)|$

Published on 23 Aug 2014 - 21:05

score 2k · Answer 7 · 2014-08-24 18:53:36

2k

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The only group of order $255$ is $\mathbb Z_{255}$ ( Using Sylow and the $N/C$ Theorem)

Published on 24 Aug 2014 - 18:53

score 1k · Answer 8 · 2014-08-25 22:28:30

1k

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The smallest composite integer $n$ such that there is a unique group of order $n$?

Published on 25 Aug 2014 - 22:28

score 920 · Answer 9 · 2014-08-25 23:03:07

920

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Smallest possible odd integer that can be the order of a non-Abelian group.

Published on 25 Aug 2014 - 23:03

score 3.1k · Answer 10 · 2014-08-26 17:23:58

3.1k

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Show that if $G$ is a group of order $168$ that has a normal subgroup of order $4$ , then $G$ has a normal subgroup of order $28$

Published on 26 Aug 2014 - 17:23

score 3.5k · Answer 11 · 2014-08-26 21:14:52

3.5k

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If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

Published on 26 Aug 2014 - 21:14

score 536 · Answer 12 · 2014-08-28 18:03:27

536

Views

Number of non isomorphic groups of order $122$, My attempt through Sylow theory.

Published on 28 Aug 2014 - 18:03

score 904 · Answer 13 · 2014-08-29 19:24:20

904

Views

A group of order $120$ has a subgroup of index $3$ or $5$ (or both)

Published on 29 Aug 2014 - 19:24

score 3.5k · Answer 14 · 2014-09-04 08:56:52

3.5k

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A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.

Published on 04 Sep 2014 - 8:56

score 53 · Answer 15 · 2014-09-07 05:46:04

53

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Two Open Ended Questions in Sylow Theory

Published on 07 Sep 2014 - 5:46

List Question

Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group

Proof of Cauchy's Lemma in the case that G is abelian

Let $G$ be finite, $H\unlhd G.$ Let $P$ be a Sylow $p$-subgroup of $H.$ Use Sylow's theorem to show $G = H N_G(P).$

Group with order $|G|=p^2q^2$ and $p\not\mid q-1, p\not\mid q+1$

Understanding what the Sylow theorems say about $p$-groups

Let $G$ be a finite group and let $a$ be an element of $G$. Then, $|cl ~(a)| = |G:C(a)|$

The only group of order $255$ is $\mathbb Z_{255}$ ( Using Sylow and the $N/C$ Theorem)

The smallest composite integer $n$ such that there is a unique group of order $n$?

Smallest possible odd integer that can be the order of a non-Abelian group.

Show that if $G$ is a group of order $168$ that has a normal subgroup of order $4$ , then $G$ has a normal subgroup of order $28$

If $H$ is a normal subgroup of a finite group $G$ and $|H|=p^k$ for some prime $p$. show that $H$ is contained in every sylow $p$ subgroup of $G$

Number of non isomorphic groups of order $122$, My attempt through Sylow theory.

A group of order $120$ has a subgroup of index $3$ or $5$ (or both)

A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.

Two Open Ended Questions in Sylow Theory

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