List questions from group-extensions

44

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What is the smallest split-simple non-simple group other than generalized quaternion groups and cyclic groups?

Published on 25 Mar 2026 - 23:37

154

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Non-abelian extensions of the Klein four-group $K_4$ by $\mathbb{Z}_2$

Published on 25 Mar 2026 - 22:04

87

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Understanding the construction of group extension

Published on 25 Mar 2026 - 20:42

117

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Understanding the construction of the split extension of group

Published on 25 Mar 2026 - 23:38

95

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Central extension of a Lie group by the circle group $\mathbb{T}$

Published on 26 Mar 2026 - 1:11

69

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Is a central extension of a torus by a torus a torus?

Published on 26 Mar 2026 - 1:10

39

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Classifying central extensions of perfect groups

Published on 10 May 2026 - 16:53

44

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$\text{GL }_2(\mathbb{Z})$ as an HNN extension

Published on 25 Mar 2026 - 20:34

18

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Central Extensions of the Quaternions

Published on 10 May 2026 - 18:04

109

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Extensions of simple Lie groups with a topological splitting

Published on 25 Mar 2026 - 22:03

66

Views

Finite image property under extensions

Published on 25 Mar 2026 - 20:34

55

Views

Difference between the concepts of extension A by B and essential extension for modules?

Published on 26 Mar 2026 - 1:06

64

Views

Help with Exercise 6.9.2 in Weibels "An introduction to Homological Algebra

Published on 26 Mar 2026 - 1:11

56

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Fibration coming from a group extension

Published on 25 Mar 2026 - 17:36

121

Views

Equivalent Definition of Solvable Groups in Serre’s Book

Published on 26 Mar 2026 - 1:03

List Question

What is the smallest split-simple non-simple group other than generalized quaternion groups and cyclic groups?

Non-abelian extensions of the Klein four-group $K_4$ by $\mathbb{Z}_2$

Understanding the construction of group extension

Understanding the construction of the split extension of group

Central extension of a Lie group by the circle group $\mathbb{T}$

Is a central extension of a torus by a torus a torus?

Classifying central extensions of perfect groups

$\text{GL }_2(\mathbb{Z})$ as an HNN extension

Central Extensions of the Quaternions

Extensions of simple Lie groups with a topological splitting

Finite image property under extensions

Difference between the concepts of extension A by B and essential extension for modules?

Help with Exercise 6.9.2 in Weibels "An introduction to Homological Algebra

Fibration coming from a group extension

Equivalent Definition of Solvable Groups in Serre’s Book

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