List questions from sylow-theory

Published on 03 Feb 2020 - 1:53

52

Views

any two Sylow p-subgroups of $GL_2(p)$ generate $SL_2(p)$?

Published on 03 Feb 2020 - 2:57

153

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If $K \triangleleft G$ and $P$ a Sylow p subgroup of a finite group $G$, then $K \cap N_G(PK)=\left\{e\right\}?$

Published on 06 Feb 2020 - 15:58

108

Views

On generalized fitting subgroup

Published on 25 Mar 2026 - 20:51

49

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Every ﬁnite group G that has a normal Sylow $2$-subgroup is solvable.

Published on 08 Feb 2020 - 3:46

772

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Nonexistence of a simple group of order 420

Published on 26 Mar 2026 - 8:03

212

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The coprime action and A-invariant Sylow p-subgroup

Published on 23 Feb 2026 - 8:39

56

Views

Centralizer of a Sylow group in the simple group of order 360

Published on 26 Mar 2026 - 2:56

224

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Hall's theorem and generalized Sylow theorem.

Published on 26 Mar 2026 - 1:09

556

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Nonexistence of a simple group of order 576

Published on 26 Mar 2026 - 2:56

165

Views

On subgroups invariant under the diagonal automorphisms

Published on 13 Feb 2020 - 4:05

107

Views

A group of order $340$ is isomorphic to $H\rtimes K$, with $K$ being a $2$-Sylow subgroup

Published on 25 Mar 2026 - 21:49

93

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Group of order $3^3$ must have a normal subgroup

Published on 19 Feb 2020 - 20:32

62

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Let $G$ be a group of order $360$. Let $A$ and $B$ be its Sylow-$2$ and Sylow-$3$ subgroups. Find the order of $A\cap B$

Published on 21 Feb 2020 - 11:51

90

Views

A group is nilpotent if all of its local subgroups are subnormal

Published on 25 Feb 2020 - 1:35

List Question

Prove a group of order $2pq$ is solvable, $p\neq q$, $p,q>2$

any two Sylow p-subgroups of $GL_2(p)$ generate $SL_2(p)$?

If $K \triangleleft G$ and $P$ a Sylow p subgroup of a finite group $G$, then $K \cap N_G(PK)=\left\{e\right\}?$

On generalized fitting subgroup

Every ﬁnite group G that has a normal Sylow $2$-subgroup is solvable.

Nonexistence of a simple group of order 420

The coprime action and A-invariant Sylow p-subgroup

Centralizer of a Sylow group in the simple group of order 360

Hall's theorem and generalized Sylow theorem.

Nonexistence of a simple group of order 576

On subgroups invariant under the diagonal automorphisms

A group of order $340$ is isomorphic to $H\rtimes K$, with $K$ being a $2$-Sylow subgroup

Group of order $3^3$ must have a normal subgroup

Let $G$ be a group of order $360$. Let $A$ and $B$ be its Sylow-$2$ and Sylow-$3$ subgroups. Find the order of $A\cap B$

A group is nilpotent if all of its local subgroups are subnormal

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