List questions from group-extensions

Published on 09 Apr 2026 - 22:42

173

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Another description for the map $\text{Ext}^1_\mathbb{Z}(A,G)\to H^2(G,A)$

Published on 12 Apr 2026 - 19:12

85

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Is the embedding problem with a cyclic kernel always solvable?

Published on 09 Apr 2026 - 13:13

1.5k

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Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups

Published on 13 Apr 2026 - 10:02

627

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Splitting in Short exact sequence

Published on 13 Apr 2026 - 19:53

286

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Group Extension Example

Published on 30 Apr 2026 - 6:35

1.5k

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Factor sets and group extensions (Homological algebra- Hilton and Stammbach VI.10.1)

Published on 15 Apr 2026 - 1:15

1.5k

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Extensions of $\mathbb{Z}$ by $\mathbb{Z}_2$

Published on 09 Apr 2026 - 2:14

53

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General formula for group extensions by an Abelian group

Published on 25 Mar 2026 - 6:02

93

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Isomorphism between free abelian groups that fit into a short exact sequence

Published on 03 May 2026 - 20:01

84

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splitting of a central extension

Published on 06 Apr 2026 - 1:48

86

Views

Torsion of simple abelian group extension

Published on 03 Apr 2026 - 20:36

143

Views

Generalization of Symmetric Group: $S_n$ to ${\bf S'}_n$

Published on 25 Mar 2026 - 6:05

67

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Galois Groups vs $\mathbb{Q}(\alpha_i)$

Published on 25 Mar 2026 - 7:33

103

Views

A morphism between two extension of a group $G$ by a group $F$ is an isomorphism. (Not sure if the terminology is standard.)

Published on 25 Mar 2026 - 6:06

List Question

How can I find $\mathbb Z_4$ as an extension of $\mathbb Z_2$ by $\mathbb Z_2$?

Another description for the map $\text{Ext}^1_\mathbb{Z}(A,G)\to H^2(G,A)$

Is the embedding problem with a cyclic kernel always solvable?

Lie Group Decomposition as Semidirect Product of Connected and Discrete Groups

Splitting in Short exact sequence

Group Extension Example

Factor sets and group extensions (Homological algebra- Hilton and Stammbach VI.10.1)

Extensions of $\mathbb{Z}$ by $\mathbb{Z}_2$

General formula for group extensions by an Abelian group

Isomorphism between free abelian groups that fit into a short exact sequence

splitting of a central extension

Torsion of simple abelian group extension

Generalization of Symmetric Group: $S_n$ to ${\bf S'}_n$

Galois Groups vs $\mathbb{Q}(\alpha_i)$

A morphism between two extension of a group $G$ by a group $F$ is an isomorphism. (Not sure if the terminology is standard.)

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