Question

What is a Simple Group?

score 325 · Answer 1 · 2026-04-11 13:59:43

325

Views

What is a Simple Group?

Published on 11 Apr 2026 - 13:59

score 147 · Answer 2 · 2026-05-10 21:13:43

147

Views

Fixed Spaces for Group Elements

Published on 10 May 2026 - 21:13

score 163 · Answer 3 · 2026-04-12 17:17:11

163

Views

Density of odd vs even group orders that are not forced to be simple by Sylow's Theorem

Published on 12 Apr 2026 - 17:17

score 909 · Answer 4 · 2026-04-09 07:32:38

909

Views

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Published on 09 Apr 2026 - 7:32

score 135 · Answer 5 · 2026-03-25 16:01:57

135

Views

There is no simple group of order $pq^2$.

Published on 25 Mar 2026 - 16:01

score 116 · Answer 6 · 2026-05-10 22:05:25

116

Views

Criterion for $PSL(2,q)$

Published on 10 May 2026 - 22:05

score 141 · Answer 7 · 2026-04-13 18:51:53

141

Views

Different attempt at proof of $A_n$ does not have a proper subgroup of index $< n$ for all $n \geq 5$

Published on 13 Apr 2026 - 18:51

score 78 · Answer 8 · 2026-05-10 16:06:37

78

Views

Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Published on 10 May 2026 - 16:06

score 102 · Answer 9 · 2026-04-12 08:45:00

102

Views

Is a direct limit of simple groups simple?

Published on 12 Apr 2026 - 8:45

score 85 · Answer 10 · 2026-03-25 19:04:44

85

Views

Show that a group of order $2^7 5^7$ cannot be simple

Published on 25 Mar 2026 - 19:04

score 411 · Answer 11 · 2026-04-17 10:22:13

411

Views

Proving that a finite simple group (order < 100) is either abelian or has order 60

Published on 17 Apr 2026 - 10:22

score 161 · Answer 12 · 2026-03-25 19:06:31

161

Views

Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

Published on 25 Mar 2026 - 19:06

score 308 · Answer 13 · 2026-04-15 20:03:54

308

Views

Using the fact that $A_n$ is simple for $n \geq 5$, prove that the only index 6 subgroups of $A_6$ and $S_6$ is $A_5$ and $S_5$ respectively

Published on 15 Apr 2026 - 20:03

score 960 · Answer 14 · 2026-04-16 01:29:29

960

Views

Prove there are no simple groups of even order $<500$ except orders $2$, $60$, $168$, and $360$.

Published on 16 Apr 2026 - 1:29

score 213 · Answer 15 · 2026-04-15 15:59:00

213

Views

Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

Published on 15 Apr 2026 - 15:59

List Question

What is a Simple Group?

Fixed Spaces for Group Elements

Density of odd vs even group orders that are not forced to be simple by Sylow's Theorem

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

There is no simple group of order $pq^2$.

Criterion for $PSL(2,q)$

Different attempt at proof of $A_n$ does not have a proper subgroup of index $< n$ for all $n \geq 5$

Number of Non-equivalent Generating Triples of Involutions in Finite Simple Groups

Is a direct limit of simple groups simple?

Show that a group of order $2^7 5^7$ cannot be simple

Proving that a finite simple group (order < 100) is either abelian or has order 60

Centralizer of a group of order 60 with $n_2=15,n_5=6,n_3=10$...

Using the fact that $A_n$ is simple for $n \geq 5$, prove that the only index 6 subgroups of $A_6$ and $S_6$ is $A_5$ and $S_5$ respectively

Prove there are no simple groups of even order $<500$ except orders $2$, $60$, $168$, and $360$.

Proof that in a simple group of order 168 the intersection of the normalizers of two distinct 7-sylows is of order 3

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