Question

Proving that the Spinor-kernel of SO3(K) is simple

score 94 · Answer 1 · 2021-11-20 20:40:40

94

Views

Proving that the Spinor-kernel of SO3(K) is simple

Published on 20 Nov 2021 - 20:40

score 61 · Answer 2 · 2021-11-24 23:40:21

61

Views

Assume $H,G$ are simple groups. Can we prove that either $H\unlhd HG$ or $H\unlhd GH$?

Published on 24 Nov 2021 - 23:40

score 105 · Answer 3 · 2026-02-24 00:49:16

105

Views

Proving that the symplectic group $Sp_{2n}(K)$ is simple if $|K|=2$ or $3$

Published on 24 Feb 2026 - 0:49

score 93 · Answer 4 · 2021-12-01 11:19:56

93

Views

If $|G| = n < 60$, and $n$ is composite, then $G$ is not a simple group. Why?

Published on 01 Dec 2021 - 11:19

score 331 · Answer 5 · 2022-01-13 22:13:59

331

Views

Growth of finite simple groups

Published on 13 Jan 2022 - 22:13

score 113 · Answer 6 · 2022-01-22 18:49:49

113

Views

If a chief factor of a group $G$ is not simple, then $G$ is not supersolvable. Is this true? If not, what is needed to make it true?

Published on 22 Jan 2022 - 18:49

score 67 · Answer 7 · 2022-01-25 01:56:26

67

Views

Which finite groups can be proved simple via this theorem?

Published on 25 Jan 2022 - 1:56

score 64 · Answer 8 · 2022-01-26 06:38:46

64

Views

Is $GL_n(\mathbb{F}_2)$ generated by a Jordan cell of size $n$ and its transpose?

Published on 26 Jan 2022 - 6:38

score 151 · Answer 9 · 2022-01-30 09:59:49

151

Views

Finding a generating set of the simple group of order 168

Published on 30 Jan 2022 - 9:59

score 667 · Answer 10 · 2022-02-05 13:23:54

667

Views

There is no simple group of order $36$.

Published on 05 Feb 2022 - 13:23

score 169 · Answer 11 · 2022-02-09 14:48:04

169

Views

Does every quasisimple finite group have a faithful complex irrep?

Published on 09 Feb 2022 - 14:48

score 137 · Answer 12 · 2022-02-18 14:55:31

137

Views

If $n\geq 5$ prove that $A_n$ is the only nontrivial normal subgroup in $S_n$. But please don't use the fact $A_n$ is simple if $n\geq 6$.

Published on 18 Feb 2022 - 14:55

score 92 · Answer 13 · 2026-03-28 06:48:25

92

Views

Showing Factor Groups are Simple; Subgroups of Solvable Groups are Solvable

Published on 28 Mar 2026 - 6:48

score 145 · Answer 14 · 2022-03-22 13:04:04

145

Views

Group of order $1320$ is not simple

Published on 22 Mar 2022 - 13:04

score 123 · Answer 15 · 2026-03-28 20:08:12

123

Views

If $S$ is a simple subnormal subgroup of $G$. Prove that if $S$ is nonabelian then $S^G$ is a direct product of simple groups isomorphic to $S$.

Published on 28 Mar 2026 - 20:08

List Question

Proving that the Spinor-kernel of SO3(K) is simple

Assume $H,G$ are simple groups. Can we prove that either $H\unlhd HG$ or $H\unlhd GH$?

Proving that the symplectic group $Sp_{2n}(K)$ is simple if $|K|=2$ or $3$

If $|G| = n < 60$, and $n$ is composite, then $G$ is not a simple group. Why?

Growth of finite simple groups

If a chief factor of a group $G$ is not simple, then $G$ is not supersolvable. Is this true? If not, what is needed to make it true?

Which finite groups can be proved simple via this theorem?

Is $GL_n(\mathbb{F}_2)$ generated by a Jordan cell of size $n$ and its transpose?

Finding a generating set of the simple group of order 168

There is no simple group of order $36$.

Does every quasisimple finite group have a faithful complex irrep?

If $n\geq 5$ prove that $A_n$ is the only nontrivial normal subgroup in $S_n$. But please don't use the fact $A_n$ is simple if $n\geq 6$.

Showing Factor Groups are Simple; Subgroups of Solvable Groups are Solvable

Group of order $1320$ is not simple

If $S$ is a simple subnormal subgroup of $G$. Prove that if $S$ is nonabelian then $S^G$ is a direct product of simple groups isomorphic to $S$.

Trending Questions

Popular # Hahtags

Popular Questions