Question

Sylow counting to show group is isomorphic to semidirect product

score 188 · Answer 1 · 2016-02-12 02:50:13

188

Views

Sylow counting to show group is isomorphic to semidirect product

Published on 12 Feb 2016 - 2:50

score 59 · Answer 2 · 2016-02-16 11:15:02

59

Views

A basic query on sylow subgroup

Published on 16 Feb 2016 - 11:15

score 2.1k · Answer 3 · 2016-02-16 22:07:12

2.1k

Views

Prove that no group of order $p^2q$ is simple where $p$ and $q$ are prime

Published on 16 Feb 2016 - 22:07

score 613 · Answer 4 · 2016-02-20 01:16:31

613

Views

Number of Sylow 3-subgroups of special linear group

Published on 20 Feb 2016 - 1:16

score 330 · Answer 5 · 2016-02-20 17:26:26

330

Views

Elements of order 2 in the special linear group

Published on 20 Feb 2016 - 17:26

score 3k · Answer 6 · 2016-02-22 04:15:06

3k

Views

When $|G|=105$ and has a normal Sylow $3-$subgroup, then $G$ is abelian.

Published on 22 Feb 2016 - 4:15

score 2.7k · Answer 7 · 2016-02-22 12:48:51

2.7k

Views

Special linear group of order $2$ over field of order $3$

Published on 22 Feb 2016 - 12:48

score 1.4k · Answer 8 · 2016-02-25 13:52:22

1.4k

Views

Let a finite group $G$ have $n (>0)$ elements of order $p$ (a prime). If the Sylow $p$-subgroup of $G$ is normal, then does $p$ divide $n+1$?

Published on 25 Feb 2016 - 13:52

score 1.2k · Answer 9 · 2016-02-25 14:51:27

1.2k

Views

Let $G$ be a group of order $p^2q^2$ , $p$ does not divide $q^2-1$ , $q$ does not divide $p^2-1$ , then is $G$ abelian?

Published on 25 Feb 2016 - 14:51

score 324 · Answer 10 · 2016-03-05 15:39:05

324

Views

Group with at least 2 subgroups of order $p$ has at least $p^2-1$ elements of order $p$.

Published on 05 Mar 2016 - 15:39

score 63 · Answer 11 · 2026-03-27 17:52:25

63

Views

ADVICE Intuition about techniques for disproving the existence of simple groups of given order

Published on 27 Mar 2026 - 17:52

score 161 · Answer 12 · 2016-03-06 00:01:21

161

Views

Clarification : No simple group for order $5103 = 3^6 \cdot 7$

Published on 06 Mar 2016 - 0:01

score 130 · Answer 13 · 2016-03-06 02:45:20

130

Views

Show that $G$ is abelian.

Published on 06 Mar 2016 - 2:45

score 134 · Answer 14 · 2016-03-06 04:17:31

134

Views

Use intersection of Sylow subgroup to prove no simple group of order 525

Published on 06 Mar 2016 - 4:17

score 714 · Answer 15 · 2016-03-07 08:54:29

714

Views

Some properties of a finite group with all Sylow subgroups that are cyclic

Published on 07 Mar 2016 - 8:54

List Question

Sylow counting to show group is isomorphic to semidirect product

A basic query on sylow subgroup

Prove that no group of order $p^2q$ is simple where $p$ and $q$ are prime

Number of Sylow 3-subgroups of special linear group

Elements of order 2 in the special linear group

When $|G|=105$ and has a normal Sylow $3-$subgroup, then $G$ is abelian.

Special linear group of order $2$ over field of order $3$

Let a finite group $G$ have $n (>0)$ elements of order $p$ (a prime). If the Sylow $p$-subgroup of $G$ is normal, then does $p$ divide $n+1$?

Let $G$ be a group of order $p^2q^2$ , $p$ does not divide $q^2-1$ , $q$ does not divide $p^2-1$ , then is $G$ abelian?

Group with at least 2 subgroups of order $p$ has at least $p^2-1$ elements of order $p$.

ADVICE Intuition about techniques for disproving the existence of simple groups of given order

Clarification : No simple group for order $5103 = 3^6 \cdot 7$

Show that $G$ is abelian.

Use intersection of Sylow subgroup to prove no simple group of order 525

Some properties of a finite group with all Sylow subgroups that are cyclic

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