List questions from sylow-theory

Published on 10 May 2026 - 14:32

140

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Sylow $p$-Subgroups and Counting Prime Numbers

Published on 13 Apr 2026 - 22:10

99

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Coprime automorphism group implies cyclic with order a cyclicity-forcing number

Published on 15 Apr 2026 - 19:15

1k

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Show that $P$ is a Sylow $p$-subgroup of $G$ if and only if $P$ is a Sylow $p$-subgroup of $N_G(P).$

Published on 16 Apr 2026 - 0:09

87

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$H_p \triangleleft G$ and $H_p \cdot H_q \triangleleft G$ then $H_q \triangleleft G$

Published on 15 Apr 2026 - 20:41

336

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Show group of order $4563=3^3\cdot13^2$ is not simple.

Published on 14 Apr 2026 - 3:18

946

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Number of normal subgroups of order $p^s$ of a $p$-group

Published on 10 May 2026 - 12:39

114

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Help proving Sylow's Theorem order 58

Published on 14 Apr 2026 - 1:48

39

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Why is there no element of $N/K$ has order a power of $p$ (except trivially the identity element)?

Published on 15 Apr 2026 - 11:15

175

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Show that a group of order 440 has a unique subgroup of order 55

Published on 16 Apr 2026 - 13:40

3.7k

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Show that no group of order 48 is simple

Published on 10 May 2026 - 14:31

198

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Show that a Sylow $q$-subgroup is normal in G, where $|G| = p^2q$.

Published on 17 Apr 2026 - 13:54

1.1k

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A 2-Sylow subgroup of $S_5$ is isomorphic to $D_4$

Published on 16 Apr 2026 - 9:46

921

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Proof of Sylow's second and third theorem from Lang's book

Published on 13 Apr 2026 - 9:39

191

Views

verification of my proof that $|G|=35$ has normal subgroups of orders 5 and 7.

Published on 13 Apr 2026 - 22:30

List Question

A group of order $p^nm$ isn't simple

Sylow $p$-Subgroups and Counting Prime Numbers

Coprime automorphism group implies cyclic with order a cyclicity-forcing number

Show that $P$ is a Sylow $p$-subgroup of $G$ if and only if $P$ is a Sylow $p$-subgroup of $N_G(P).$

$H_p \triangleleft G$ and $H_p \cdot H_q \triangleleft G$ then $H_q \triangleleft G$

Show group of order $4563=3^3\cdot13^2$ is not simple.

Number of normal subgroups of order $p^s$ of a $p$-group

Help proving Sylow's Theorem order 58

Why is there no element of $N/K$ has order a power of $p$ (except trivially the identity element)?

Show that a group of order 440 has a unique subgroup of order 55

Show that no group of order 48 is simple

Show that a Sylow $q$-subgroup is normal in G, where $|G| = p^2q$.

A 2-Sylow subgroup of $S_5$ is isomorphic to $D_4$

Proof of Sylow's second and third theorem from Lang's book

verification of my proof that $|G|=35$ has normal subgroups of orders 5 and 7.

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