List questions from sylow-theory

Published on 20 Aug 2016 - 11:05

268

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If $|G| = p_1^{r_1}...p_k^{r_k}$ it is the direct internal product of its Sylow subgroups

Published on 20 Aug 2016 - 12:13

171

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How do you prove $(P_1...P_{r-1}) \cap P_r = \{ e \}$ for normal Sylow subgroups $P_i$?

Published on 21 Aug 2016 - 0:49

1.2k

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A group of order 2010 has a normal subgroup of order 5

Published on 21 Aug 2016 - 3:41

59

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Need help with the follow lemma in Sylow theorems

Published on 25 Aug 2016 - 0:53

213

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Need help with the proof of Sylow's First Theorem

Published on 25 Aug 2016 - 5:39

447

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Problem about solvable groups

Published on 26 Mar 2026 - 19:14

80

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Question from Herstein's Topics in Algebra on Sylow subgroups

Published on 29 Aug 2016 - 23:19

133

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Does Sylow's theorem give an upper bound for the number of isomorphism classes?

Published on 30 Aug 2016 - 18:17

306

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Normal Sylow subgroup P has a complement in G (no Schur–Zassenhaus)

Published on 06 Sep 2016 - 16:10

32

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p divides number of p-roots in a finite group

Published on 15 Sep 2016 - 22:57

475

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Normalizer of Normalizer

Published on 16 Sep 2016 - 12:14

136

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$p$-Sylow subgroup of $S_{p^3}$

Published on 25 Mar 2026 - 6:11

1k

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Show that the center of a group of order 60 cannot have order 4?

Published on 23 Sep 2016 - 15:33

260

Views

Prove Group of square-free order has normal Sylow Subgroup by counting elements

Published on 26 Sep 2016 - 10:55

List Question

The conjugate of a sylow $p$-subgroup is a sylow $p$-subgroup

If $|G| = p_1^{r_1}...p_k^{r_k}$ it is the direct internal product of its Sylow subgroups

How do you prove $(P_1...P_{r-1}) \cap P_r = \{ e \}$ for normal Sylow subgroups $P_i$?

A group of order 2010 has a normal subgroup of order 5

Need help with the follow lemma in Sylow theorems

Need help with the proof of Sylow's First Theorem

Problem about solvable groups

Question from Herstein's Topics in Algebra on Sylow subgroups

Does Sylow's theorem give an upper bound for the number of isomorphism classes?

Normal Sylow subgroup P has a complement in G (no Schur–Zassenhaus)

p divides number of p-roots in a finite group

Normalizer of Normalizer

$p$-Sylow subgroup of $S_{p^3}$

Show that the center of a group of order 60 cannot have order 4?

Prove Group of square-free order has normal Sylow Subgroup by counting elements

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