List questions from sylow-theory

Published on 03 Nov 2019 - 21:16

85

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Show that a group of order $2^7 5^7$ cannot be simple

Published on 25 Mar 2026 - 19:04

86

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Show that every group of order 1965 is isomorphic to $\mathbb{Z}/393\mathbb{Z} \rtimes \mathbb{Z}/5\mathbb{Z} $

Published on 25 Mar 2026 - 18:49

46

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How to show that the centralizer formed by $g\in A\cap B$ where $A$ and $B$ are 3-Sylow subgroups contains $A$ and $B.$

Published on 05 Nov 2019 - 23:35

132

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group of order $p\cdot q^{2}\cdot r$, where $p,q,r$ are primes with $p<q<r$.

Published on 06 Nov 2019 - 11:05

161

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Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

Published on 25 Mar 2026 - 19:06

149

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How to find a p-Sylow for symmetric group $S_{p^2}$？

Published on 25 Mar 2026 - 18:48

393

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Sylow $p$-subgroup is cyclic

Published on 10 Nov 2019 - 8:44

321

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How to find a 2-Sylow subgroup of $GL_2(F_3)$?

Published on 22 Mar 2026 - 10:18

353

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Sylow theorem and tetrahedron

Published on 10 Nov 2019 - 15:19

74

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Conjugacy class's cardinalities' property.

Published on 11 Nov 2019 - 2:18

53

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On $p$-Sylows for $S_{2p}$ ... $S_{(p-1)p}$

Published on 11 Nov 2019 - 6:46

327

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$P,Q$ Sylow subgroups $\implies$ $PQ$ a subgroup

Published on 12 Nov 2019 - 5:12

71

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Did I correctly prove this?(Group theory)

Published on 13 Nov 2019 - 4:53

211

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Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

Published on 25 Mar 2026 - 17:44

List Question

Show that a group of order $2016=2^5 3^2 7$ is not simple

Show that a group of order $2^7 5^7$ cannot be simple

Show that every group of order 1965 is isomorphic to $\mathbb{Z}/393\mathbb{Z} \rtimes \mathbb{Z}/5\mathbb{Z} $

How to show that the centralizer formed by $g\in A\cap B$ where $A$ and $B$ are 3-Sylow subgroups contains $A$ and $B.$

group of order $p\cdot q^{2}\cdot r$, where $p,q,r$ are primes with $p<q<r$.

Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

How to find a p-Sylow for symmetric group $S_{p^2}$？

Sylow $p$-subgroup is cyclic

How to find a 2-Sylow subgroup of $GL_2(F_3)$?

Sylow theorem and tetrahedron

Conjugacy class's cardinalities' property.

On $p$-Sylows for $S_{2p}$ ... $S_{(p-1)p}$

$P,Q$ Sylow subgroups $\implies$ $PQ$ a subgroup

Did I correctly prove this?(Group theory)

Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

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