List questions from sylow-theory

Published on 26 Mar 2026 - 19:05

63

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A group may have two distinct characteristic Sylow-$p$-subgroups

Published on 23 Feb 2026 - 5:42

211

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Show that in a group $G$ of order $165=3\cdot 5\cdot 11$, the center $Z(G)$ contains a subgroup of order 11.

Published on 27 Jul 2023 - 19:04

111

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Number of Sylow subgroups in $p$-solvable groups - Navarro article

Published on 26 Mar 2026 - 19:01

84

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Sylow $p$-subgroup and Sylow $q$-subgroup both normal

Published on 03 Aug 2023 - 23:15

96

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Let $H,K \leq G$ s.t $H,K$ two different Sylow $p$-subgroups of $G$. Prove $HK$ isn't a subgroup of $G$.

Published on 15 Aug 2023 - 8:49

117

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Show that a group of order $2010$ with an abelian normal subgroup of order $6$ is abelian

Published on 30 Aug 2023 - 8:04

109

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Group of order 231, show the existence of a normal subgroup of order 21

Published on 30 Aug 2023 - 13:46

120

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3 divides the cardinality of the center of a group of order 225

Published on 30 Aug 2023 - 21:36

81

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Question on the classification of groups of order 102

Published on 02 Sep 2023 - 7:43

45

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Theorem Reference Query: $p'$-Elements in Supersolvable Groups

Published on 03 Sep 2023 - 21:50

115

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2-Sylow subgroup of $S_6$.

Published on 09 Sep 2023 - 16:22

54

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Characteristic subgroups of a group of order 6 or 12

Published on 23 Feb 2026 - 5:46

50

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Some questions about the proof of the First Sylow theorem

Published on 21 Sep 2023 - 23:25

134

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Group of quaternions $Q_8$ is not a subgroup of $S_4$

Published on 23 Sep 2023 - 13:22

List Question

Group of order $1575$ is solvable

A group may have two distinct characteristic Sylow-$p$-subgroups

Show that in a group $G$ of order $165=3\cdot 5\cdot 11$, the center $Z(G)$ contains a subgroup of order 11.

Number of Sylow subgroups in $p$-solvable groups - Navarro article

Sylow $p$-subgroup and Sylow $q$-subgroup both normal

Let $H,K \leq G$ s.t $H,K$ two different Sylow $p$-subgroups of $G$. Prove $HK$ isn't a subgroup of $G$.

Show that a group of order $2010$ with an abelian normal subgroup of order $6$ is abelian

Group of order 231, show the existence of a normal subgroup of order 21

3 divides the cardinality of the center of a group of order 225

Question on the classification of groups of order 102

Theorem Reference Query: $p'$-Elements in Supersolvable Groups

2-Sylow subgroup of $S_6$.

Characteristic subgroups of a group of order 6 or 12

Some questions about the proof of the First Sylow theorem

Group of quaternions $Q_8$ is not a subgroup of $S_4$

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