Question

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

score 1.3k · Answer 1 · 2026-04-13 09:07:58

1.3k

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

Published on 13 Apr 2026 - 9:07

score 71 · Answer 2 · 2026-04-17 04:16:15

71

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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 17 Apr 2026 - 4:16

score 226 · Answer 3 · 2026-05-10 18:03:50

226

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About Sylow subgroup and internal direct product.

Published on 10 May 2026 - 18:03

score 71 · Answer 4 · 2026-04-12 09:11:45

71

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Relationship between prime power and the divisor

Published on 12 Apr 2026 - 9:11

score 83 · Answer 5 · 2026-04-16 13:45:45

83

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

Published on 16 Apr 2026 - 13:45

score 161 · Answer 6 · 2026-04-14 07:38:49

161

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Sylow's First Theorem acting on Abelian Group

Published on 14 Apr 2026 - 7:38

score 77 · Answer 7 · 2026-04-12 15:25:50

77

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Group Theory (Sylow p-subgroups questions)

Published on 12 Apr 2026 - 15:25

score 56 · Answer 8 · 2026-04-10 12:21:35

56

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

Published on 10 Apr 2026 - 12:21

score 155 · Answer 9 · 2026-04-16 13:39:45

155

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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 16 Apr 2026 - 13:39

score 53 · Answer 10 · 2026-04-16 17:31:59

53

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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 16 Apr 2026 - 17:31

score 192 · Answer 11 · 2026-04-15 23:51:02

192

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Group Isomorphism regarding Sylow Subgroups

Published on 15 Apr 2026 - 23:51

score 2.1k · Answer 12 · 2026-04-17 14:20:20

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 17 Apr 2026 - 14:20

score 1.5k · Answer 13 · 2026-04-11 20:22:09

1.5k

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Proof that no group of order $525$ is simple

Published on 11 Apr 2026 - 20:22

score 330 · Answer 14 · 2026-04-16 10:10:19

330

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

Published on 16 Apr 2026 - 10:10

score 575 · Answer 15 · 2026-04-11 14:35:06

575

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Question about p-Sylow subgroups being maximal

Published on 11 Apr 2026 - 14:35

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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