List questions from sylow-theory

Published on 06 Apr 2015 - 14:03

83

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Proof of normal subgroup

Published on 09 Apr 2015 - 21:33

751

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$G$ is a finite group,with eight Sylow 7 subgroups. Show that there exists a normal subgroup $N$ of $G$ s.t. index $[G:N]$ divisible by 56, not by 49.

Published on 10 Apr 2015 - 17:34

237

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Various Intersections of Sylow p-subgroups.

Published on 13 Apr 2015 - 20:37

88

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Sylow counting - classifying groups of order 15

Published on 15 Apr 2015 - 17:42

84

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Sylow's theorem and uniqueness of normal supgroup

Published on 16 Apr 2015 - 4:40

2.3k

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Construct Group of Order 21 Without Semi Product

Published on 23 Apr 2015 - 0:43

7.3k

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Difference between definitions of $p$-subgroup and Sylow $p$-subgroup

Published on 26 Mar 2026 - 14:41

162

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Sylow p-subgroups and set X not divisible by p

Published on 27 Apr 2015 - 1:20

740

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Number of Sylow $p$-subgroups of a direct product of groups

Published on 05 May 2015 - 5:57

464

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$|G|=p_1p_2p_3$ distinct primes with $p_i \nmid p_j-1$ then $G$ is cyclic

Published on 05 May 2015 - 14:26

507

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Group of order $135$ abelian and not cyclic

Published on 07 May 2015 - 14:29

851

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Direct product and Sylow subgroups

Published on 09 May 2015 - 13:52

2.1k

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Maximum number of Sylow subgroups

Published on 12 May 2015 - 9:43

435

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Must a non-simple group have a normal Sylow subgroup?

Published on 27 Mar 2026 - 5:58

List Question

What is a group action, and how can we apply it to Sylow theory

Proof of normal subgroup

$G$ is a finite group,with eight Sylow 7 subgroups. Show that there exists a normal subgroup $N$ of $G$ s.t. index $[G:N]$ divisible by 56, not by 49.

Various Intersections of Sylow p-subgroups.

Sylow counting - classifying groups of order 15

Sylow's theorem and uniqueness of normal supgroup

Construct Group of Order 21 Without Semi Product

Difference between definitions of $p$-subgroup and Sylow $p$-subgroup

Sylow p-subgroups and set X not divisible by p

Number of Sylow $p$-subgroups of a direct product of groups

$|G|=p_1p_2p_3$ distinct primes with $p_i \nmid p_j-1$ then $G$ is cyclic

Group of order $135$ abelian and not cyclic

Direct product and Sylow subgroups

Maximum number of Sylow subgroups

Must a non-simple group have a normal Sylow subgroup?

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