Question

With reference to an action between sylow subgroups

score 49 · Answer 1 · 2019-07-04 05:29:22

49

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With reference to an action between sylow subgroups

Published on 04 Jul 2019 - 5:29

score 1k · Answer 2 · 2019-07-04 15:51:18

1k

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$G$ is a finite group s.t. $(ab)^p=a^pb^p$; $P$ is its $p$-Sylow subgroup. Then there exists $N \unlhd G$ such that $N \cap P = (e)$ and $NP=G$.

Published on 04 Jul 2019 - 15:51

score 1k · Answer 3 · 2019-07-05 12:15:15

1k

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Does a group of order $400$ always have a subgroup of order $200$?

Published on 05 Jul 2019 - 12:15

score 277 · Answer 4 · 2019-07-05 20:32:47

277

Views

Sylow-$3$-subgroups of group of order $117 = 3^2 \cdot 13$

Published on 05 Jul 2019 - 20:32

score 947 · Answer 5 · 2019-07-06 20:38:20

947

Views

Show that a finite abelian group is cyclic if and only if every Sylow-p-subgroups are cyclic.

Published on 06 Jul 2019 - 20:38

score 877 · Answer 6 · 2026-03-25 04:40:32

877

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Find all the groups of order 28

Published on 25 Mar 2026 - 4:40

score 1.1k · Answer 7 · 2019-07-12 12:41:24

1.1k

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If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

Published on 12 Jul 2019 - 12:41

score 264 · Answer 8 · 2019-07-13 04:15:39

264

Views

Any group of order $p^2q^2$ is not simple for $p,q$ prime

Published on 13 Jul 2019 - 4:15

score 3k · Answer 9 · 2019-07-20 15:41:25

3k

Views

Let G be a group of order $pqr$,where $p<q<r$ are primes. Prove that the Sylow r-group is normal.

Published on 20 Jul 2019 - 15:41

score 345 · Answer 10 · 2019-07-24 08:11:09

345

Views

A question about groups of order $504=2^3\cdot 3^2 \cdot 7$

Published on 24 Jul 2019 - 8:11

score 995 · Answer 11 · 2026-02-23 04:47:28

995

Views

Why the normalizer of the Sylow $p$-subgroups of the symmetric group of degree $p$ has order $p(p-1)$ and is known as Frobenius group $F_{p(p-1)}$?

Published on 23 Feb 2026 - 4:47

score 324 · Answer 12 · 2019-07-30 01:46:25

324

Views

Faithful Action using Sylow Subgroups

Published on 30 Jul 2019 - 1:46

score 770 · Answer 13 · 2019-07-30 02:58:50

770

Views

Is finite group isomorphic with the direct prouct of the Sylow $p$ subgroups?

Published on 30 Jul 2019 - 2:58

score 113 · Answer 14 · 2019-07-31 08:35:26

113

Views

Does every Sylow Subgroup have same cardinality?

Published on 31 Jul 2019 - 8:35

score 189 · Answer 15 · 2019-08-02 01:32:35

189

Views

Proof of Sylow's Theorem

Published on 02 Aug 2019 - 1:32

List Question

With reference to an action between sylow subgroups

$G$ is a finite group s.t. $(ab)^p=a^pb^p$; $P$ is its $p$-Sylow subgroup. Then there exists $N \unlhd G$ such that $N \cap P = (e)$ and $NP=G$.

Does a group of order $400$ always have a subgroup of order $200$?

Sylow-$3$-subgroups of group of order $117 = 3^2 \cdot 13$

Show that a finite abelian group is cyclic if and only if every Sylow-p-subgroups are cyclic.

Find all the groups of order 28

If $|G|=36$ then $G$ has either a normal $2$-Sylow or a normal $3$-Sylow

Any group of order $p^2q^2$ is not simple for $p,q$ prime

Let G be a group of order $pqr$,where $p<q<r$ are primes. Prove that the Sylow r-group is normal.

A question about groups of order $504=2^3\cdot 3^2 \cdot 7$

Why the normalizer of the Sylow $p$-subgroups of the symmetric group of degree $p$ has order $p(p-1)$ and is known as Frobenius group $F_{p(p-1)}$?

Faithful Action using Sylow Subgroups

Is finite group isomorphic with the direct prouct of the Sylow $p$ subgroups?

Does every Sylow Subgroup have same cardinality?

Proof of Sylow's Theorem

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