Question

Let $K\lhd G$ be s.t. both $K$ and $G/K$ are simple. Show that either $K$ is the only proper normal subgroup of $G$, or $G \cong K \times (G / K)$.

score 152 · Answer 1 · 2024-02-04 04:17:10

152

Views

Let $K\lhd G$ be s.t. both $K$ and $G/K$ are simple. Show that either $K$ is the only proper normal subgroup of $G$, or $G \cong K \times (G / K)$.

Published on 04 Feb 2024 - 4:17

score 67 · Answer 2 · 2024-02-05 17:24:58

67

Views

An example of non simple group which is also a Lie group such that $G$ is a connected Lie group and has no non trivial normal Lie subgroup

Published on 05 Feb 2024 - 17:24

score 63 · Answer 3 · 2024-02-10 10:06:17

63

Views

"$S$ is the unique irreducible $\operatorname{End}(S)$-module"

Published on 10 Feb 2024 - 10:06

score 84 · Answer 4 · 2024-02-13 15:05:32

84

Views

Isomorphic two abelian subgroups which lies in the some finite union of conjugacy classes of simple group

Published on 13 Feb 2024 - 15:05

score 4.4k · Answer 5 · 2015-01-05 14:13:52

4.4k

Views

There is no simple group of order $144$

Published on 05 Jan 2015 - 14:13

score 1.3k · Answer 6 · 2015-01-07 13:20:14

1.3k

Views

No group of order $400$ is simple - clarification

Published on 07 Jan 2015 - 13:20

score 1.6k · Answer 7 · 2015-01-07 15:00:23

1.6k

Views

Find a composition series of $D_8$

Published on 07 Jan 2015 - 15:00

score 452 · Answer 8 · 2015-01-09 14:15:17

452

Views

What is the composition series of $\mathbb Z_7$ x $\mathbb Z_{12}$

Published on 09 Jan 2015 - 14:15

score 1.5k · Answer 9 · 2015-01-11 19:30:21

1.5k

Views

Find number of Sylow $3$ and Sylow $5$ subgroups of a simple Group, $G$ of order $60$

Published on 11 Jan 2015 - 19:30

score 249 · Answer 10 · 2026-03-26 12:53:01

249

Views

An example of a simple infinite $2$-group

Published on 26 Mar 2026 - 12:53

score 2.6k · Answer 11 · 2015-01-20 14:08:05

2.6k

Views

Direct product of simple groups

Published on 20 Jan 2015 - 14:08

score 53 · Answer 12 · 2015-01-28 13:44:51

53

Views

Why $n_i=j$ implies that there is a subgroup $H$ of $G$ of index j?

Published on 28 Jan 2015 - 13:44

score 1.4k · Answer 13 · 2015-03-12 18:23:02

1.4k

Views

$G$ is a simple group of order $60$.Then $G$ contains a subgroup of order 12

Published on 12 Mar 2015 - 18:23

score 372 · Answer 14 · 2015-03-12 18:40:22

372

Views

Any simple group of order 60 is isomorphic to $A_5$

Published on 12 Mar 2015 - 18:40

score 435 · Answer 15 · 2015-04-30 05:07:16

435

Views

How did we classify the finite simple groups when we haven't classified the primes?

Published on 30 Apr 2015 - 5:07

List Question

Let $K\lhd G$ be s.t. both $K$ and $G/K$ are simple. Show that either $K$ is the only proper normal subgroup of $G$, or $G \cong K \times (G / K)$.

An example of non simple group which is also a Lie group such that $G$ is a connected Lie group and has no non trivial normal Lie subgroup

"$S$ is the unique irreducible $\operatorname{End}(S)$-module"

Isomorphic two abelian subgroups which lies in the some finite union of conjugacy classes of simple group

There is no simple group of order $144$

No group of order $400$ is simple - clarification

Find a composition series of $D_8$

What is the composition series of $\mathbb Z_7$ x $\mathbb Z_{12}$

Find number of Sylow $3$ and Sylow $5$ subgroups of a simple Group, $G$ of order $60$

An example of a simple infinite $2$-group

Direct product of simple groups

Why $n_i=j$ implies that there is a subgroup $H$ of $G$ of index j?

$G$ is a simple group of order $60$.Then $G$ contains a subgroup of order 12

Any simple group of order 60 is isomorphic to $A_5$

How did we classify the finite simple groups when we haven't classified the primes?

Trending Questions

Popular # Hahtags

Popular Questions