Question

How big must the union of a group's Sylow p-subgroups be?

score 1.3k · Answer 1 · 2018-11-14 05:21:48

1.3k

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How big must the union of a group's Sylow p-subgroups be?

Published on 14 Nov 2018 - 5:21

score 68 · Answer 2 · 2018-11-14 23:13:51

68

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Let $p$ be a prime dividing $|G|$, and let $S_p$ be a $p$-Sylow subgroup of $G$. Show that $N(N(S_p))=N(S_p)$.

Published on 14 Nov 2018 - 23:13

score 222 · Answer 3 · 2018-11-15 17:11:54

222

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About Sylow subgroup and internal direct product.

Published on 15 Nov 2018 - 17:11

score 68 · Answer 4 · 2018-11-16 07:56:27

68

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Relationship between prime power and the divisor

Published on 16 Nov 2018 - 7:56

score 80 · Answer 5 · 2018-11-16 15:27:14

80

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Equivalent conditions for a Group $G$ with order $p^2q$ ( with $p>q$ both prime) be abelian.

Published on 16 Nov 2018 - 15:27

score 158 · Answer 6 · 2018-11-17 08:56:14

158

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Sylow's First Theorem acting on Abelian Group

Published on 17 Nov 2018 - 8:56

score 74 · Answer 7 · 2018-11-20 18:17:32

74

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Group Theory (Sylow p-subgroups questions)

Published on 20 Nov 2018 - 18:17

score 54 · Answer 8 · 2018-11-20 19:30:31

54

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Is $n_p(G)$ unique for different groups of size $p$?

Published on 20 Nov 2018 - 19:30

score 152 · Answer 9 · 2018-11-22 14:02:03

152

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$x,y \in Z_G(P)$ such that $gxg^{-1}=y$, show that there exists $n\in N_G(P)$ such that $nxn^{-1}=y$.

Published on 22 Nov 2018 - 14:02

score 50 · Answer 10 · 2018-11-26 14:22:39

50

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$gcd(p,m-1)=gcd(p-1,m)=1$ if and only if G has a normal Sylow p-subgroup in $Z(G)$

Published on 26 Nov 2018 - 14:22

score 189 · Answer 11 · 2018-12-05 19:06:40

189

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Group Isomorphism regarding Sylow Subgroups

Published on 05 Dec 2018 - 19:06

score 2.1k · Answer 12 · 2018-12-06 17:50:46

2.1k

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Let H be a Sylow p-subgroup of G. Prove that H is the only Sylow p-subgroup of G contained in N(H).

Published on 06 Dec 2018 - 17:50

score 1.5k · Answer 13 · 2018-12-06 19:13:07

1.5k

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Proof that no group of order $525$ is simple

Published on 06 Dec 2018 - 19:13

score 327 · Answer 14 · 2018-12-07 20:24:52

327

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Group of order $6p^m$ is solvable for primes $p\geq 2$

Published on 07 Dec 2018 - 20:24

score 572 · Answer 15 · 2018-12-08 04:22:17

572

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Question about p-Sylow subgroups being maximal

Published on 08 Dec 2018 - 4:22

List Question

How big must the union of a group's Sylow p-subgroups be?

Let $p$ be a prime dividing $|G|$, and let $S_p$ be a $p$-Sylow subgroup of $G$. Show that $N(N(S_p))=N(S_p)$.

About Sylow subgroup and internal direct product.

Relationship between prime power and the divisor

Equivalent conditions for a Group $G$ with order $p^2q$ ( with $p>q$ both prime) be abelian.

Sylow's First Theorem acting on Abelian Group

Group Theory (Sylow p-subgroups questions)

Is $n_p(G)$ unique for different groups of size $p$?

$x,y \in Z_G(P)$ such that $gxg^{-1}=y$, show that there exists $n\in N_G(P)$ such that $nxn^{-1}=y$.

$gcd(p,m-1)=gcd(p-1,m)=1$ if and only if G has a normal Sylow p-subgroup in $Z(G)$

Group Isomorphism regarding Sylow Subgroups

Let H be a Sylow p-subgroup of G. Prove that H is the only Sylow p-subgroup of G contained in N(H).

Proof that no group of order $525$ is simple

Group of order $6p^m$ is solvable for primes $p\geq 2$

Question about p-Sylow subgroups being maximal

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