List questions from sylow-theory

Published on 17 Jan 2020 - 14:47

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Group of order 2020

Published on 17 Jan 2020 - 18:48

216

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Why is so important "to count" the number of the (all isomorphic to each other) Sylow $p$-subgroups?

Published on 20 Jan 2020 - 8:20

94

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Lemma for Sylow-Theorem

Published on 21 Jan 2020 - 18:59

34

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Lemma about Sylowgroups of Subgroups

Published on 22 Jan 2020 - 11:28

76

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$SL_{2}(\mathbb{F}_{q})$ does not have periodic cohomology.

Published on 26 Mar 2026 - 21:09

46

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Equality for Normalizer and Subgroup

Published on 22 Jan 2020 - 13:28

84

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Prove that a group of order 45 is necessarily abelian by Sylows' Theorems

Published on 23 Jan 2020 - 21:49

78

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Question on proof $G$ is not simple

Published on 26 Mar 2026 - 3:00

100

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Group of order 380 is not simple

Published on 25 Jan 2020 - 8:05

51

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Index of Hall subgroup divides normalizer of center of Sylow-p subgroup

Published on 27 Jan 2020 - 21:32

473

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Determine the Sylow $p$-subgroups of $SL(2, \mathbb{F}_5)$

Published on 28 Jan 2020 - 12:13

255

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If $P\le G$ is a sylow-$p$ and $Q$ is any $p$ subgroup, then $Q\cap P = Q\cap N(P).$

Published on 25 Mar 2026 - 19:12

77

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Invariant Sylow subgroups and solvability of finite groups

Published on 23 Feb 2026 - 8:39

161

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Reference request for self study of class equation and Sylow theorem.

Published on 01 Feb 2020 - 11:37

List Question

$\frac{HS}{H\cap S}$ is a Sylow $p-$subgroup of $\frac{G}{H}$.

Group of order 2020

Why is so important "to count" the number of the (all isomorphic to each other) Sylow $p$-subgroups?

Lemma for Sylow-Theorem

Lemma about Sylowgroups of Subgroups

$SL_{2}(\mathbb{F}_{q})$ does not have periodic cohomology.

Equality for Normalizer and Subgroup

Prove that a group of order 45 is necessarily abelian by Sylows' Theorems

Question on proof $G$ is not simple

Group of order 380 is not simple

Index of Hall subgroup divides normalizer of center of Sylow-p subgroup

Determine the Sylow $p$-subgroups of $SL(2, \mathbb{F}_5)$

If $P\le G$ is a sylow-$p$ and $Q$ is any $p$ subgroup, then $Q\cap P = Q\cap N(P).$

Invariant Sylow subgroups and solvability of finite groups

Reference request for self study of class equation and Sylow theorem.

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