Question

A group of order $p^nm$ isn't simple

score 893 · Answer 1 · 2026-04-14 20:48:02

893

Views

A group of order $p^nm$ isn't simple

Published on 14 Apr 2026 - 20:48

score 932 · Answer 2 · 2026-04-09 22:58:58

932

Views

How to show that Group of order $2376$ is not simple

Published on 09 Apr 2026 - 22:58

score 1.2k · Answer 3 · 2026-04-15 03:49:48

1.2k

Views

When a simple group normalizes a subnormal subgroup of a finite group

Published on 15 Apr 2026 - 3:49

score 372 · Answer 4 · 2026-04-13 17:33:54

372

Views

What is the connection between simple groups, composition series, and solvable groups?

Published on 13 Apr 2026 - 17:33

score 140 · Answer 5 · 2026-04-15 00:32:41

140

Views

If $G$ is a simple group of order $60$, how can we there exists some $G\to A_6$ not trivial without using the fact that $G\cong A_5$?

Published on 15 Apr 2026 - 0:32

score 3.7k · Answer 6 · 2026-04-13 09:10:04

3.7k

Views

Show that no group of order 48 is simple

Published on 13 Apr 2026 - 9:10

score 330 · Answer 7 · 2026-04-14 09:50:58

330

Views

Show a group cannot have order $2n$ for some odd $n\gt 1$ and be simple (without Cauchy's Theorem)

Published on 14 Apr 2026 - 9:50

score 425 · Answer 8 · 2026-04-15 19:28:24

425

Views

Minimum size of index of a proper subgroup of a finite, non-abelian simple group $G$

Published on 15 Apr 2026 - 19:28

score 339 · Answer 9 · 2026-04-16 04:28:09

339

Views

If $H$ is a subgroup with prime index $p$ of a finite simple group $G$, then $p$ is the maximal prime $p$ dividing $|G|$.

Published on 16 Apr 2026 - 4:28

score 731 · Answer 10 · 2026-04-17 03:17:18

731

Views

If all homomorphisms $f:G→H$ are trivial or injective, then G is simple.

Published on 17 Apr 2026 - 3:17

score 130 · Answer 11 · 2026-04-13 00:17:59

130

Views

The cases in proving that a group of order 90 is not simple

Published on 13 Apr 2026 - 0:17

score 157 · Answer 12 · 2026-04-14 11:29:37

157

Views

No group of order 10000 is simple

Published on 14 Apr 2026 - 11:29

score 708 · Answer 13 · 2026-04-11 23:04:49

708

Views

On automorphisms of groups which extend as automorphisms to every larger group

Published on 11 Apr 2026 - 23:04

score 59 · Answer 14 · 2026-04-16 01:35:58

59

Views

When does a simple Lie group contain a nonsimple subgroup?

Published on 16 Apr 2026 - 1:35

score 643 · Answer 15 · 2026-04-15 09:52:32

643

Views

Relation between the order of an element of a group and their character in a simple group

Published on 15 Apr 2026 - 9:52

List Question

A group of order $p^nm$ isn't simple

How to show that Group of order $2376$ is not simple

When a simple group normalizes a subnormal subgroup of a finite group

What is the connection between simple groups, composition series, and solvable groups?

If $G$ is a simple group of order $60$, how can we there exists some $G\to A_6$ not trivial without using the fact that $G\cong A_5$?

Show that no group of order 48 is simple

Show a group cannot have order $2n$ for some odd $n\gt 1$ and be simple (without Cauchy's Theorem)

Minimum size of index of a proper subgroup of a finite, non-abelian simple group $G$

If $H$ is a subgroup with prime index $p$ of a finite simple group $G$, then $p$ is the maximal prime $p$ dividing $|G|$.

If all homomorphisms $f:G→H$ are trivial or injective, then G is simple.

The cases in proving that a group of order 90 is not simple

No group of order 10000 is simple

On automorphisms of groups which extend as automorphisms to every larger group

When does a simple Lie group contain a nonsimple subgroup?

Relation between the order of an element of a group and their character in a simple group

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