List questions from sylow-theory

Published on 29 Jul 2018 - 15:05

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Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Published on 30 Jul 2018 - 23:55

53

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Find two finite groups $G_1$ and $G_2$ such as:

Published on 03 Aug 2018 - 11:44

35

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Let $G=\langle (1,2,3,4,5,6,7), (2,4,3,7,5,6) \rangle$

Published on 03 Aug 2018 - 13:02

144

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Let $A \unlhd G$, then $n_p(G)=n_p(G/A)n_p(PA)$ for $P\in Syl_p(G)$ and $n_p(PA)=|A:N_A(P)|$

Published on 06 Aug 2018 - 3:23

123

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$3$-Sylow subgroup of $SL(n, \mathbb{F}_3)$

Published on 06 Aug 2018 - 20:36

966

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A finite group of even order, whose $2$-Sylow subgroups are cyclic, is not simple.

Published on 25 Mar 2026 - 0:07

127

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Finite group with cyclic Sylow-2 group has a normal subgroup of index 2.

Published on 11 Aug 2018 - 8:09

664

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Understanding Proof of Sylow theorem from Herstein

Published on 11 Aug 2018 - 9:21

97

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First Sylow Theorem proof

Published on 12 Aug 2018 - 7:51

850

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Can one prove that a group of order 150 is not simple using element counting?

Published on 25 Mar 2026 - 0:01

290

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Why does $A_5$ have $\binom{5}{4}$ Sylow 2-subgroups?

Published on 13 Aug 2018 - 14:17

1.3k

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Every Abelian group with order a product of two different primes is cyclic.

Published on 01 Sep 2018 - 16:17

55

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How to guarantee non existence of order 4 elements in class group of a maximal order

Published on 19 Mar 2026 - 23:32

1.2k

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A group of order $36$ has either a normal Sylow $2$-subgroup or a normal Sylow $3$-subgroup

Published on 15 Sep 2018 - 22:00

List Question

P-sylow subgroups of group of order $340$

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Find two finite groups $G_1$ and $G_2$ such as:

Let $G=\langle (1,2,3,4,5,6,7), (2,4,3,7,5,6) \rangle$

Let $A \unlhd G$, then $n_p(G)=n_p(G/A)n_p(PA)$ for $P\in Syl_p(G)$ and $n_p(PA)=|A:N_A(P)|$

$3$-Sylow subgroup of $SL(n, \mathbb{F}_3)$

A finite group of even order, whose $2$-Sylow subgroups are cyclic, is not simple.

Finite group with cyclic Sylow-2 group has a normal subgroup of index 2.

Understanding Proof of Sylow theorem from Herstein

First Sylow Theorem proof

Can one prove that a group of order 150 is not simple using element counting?

Why does $A_5$ have $\binom{5}{4}$ Sylow 2-subgroups?

Every Abelian group with order a product of two different primes is cyclic.

How to guarantee non existence of order 4 elements in class group of a maximal order

A group of order $36$ has either a normal Sylow $2$-subgroup or a normal Sylow $3$-subgroup

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