List questions from group-extensions

Published on 10 Apr 2026 - 15:01

110

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Functoriality of Lyndon-Hochschild-Serre spectral sequences in coefficients.

Published on 15 Apr 2026 - 3:24

140

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The extension of a connected, simply-connected Lie group by $\mathbb{Z}$ is trivial.

Published on 12 Apr 2026 - 21:11

175

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On the central extension of a group

Published on 15 Apr 2026 - 8:14

138

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Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent

Published on 09 Apr 2026 - 18:31

112

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Find isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent

Published on 11 Apr 2026 - 8:38

102

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Extension that split for all p-Sylow

Published on 12 Apr 2026 - 6:56

121

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Is there always a way to break a group?

Published on 27 Mar 2026 - 13:00

180

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Showing that any central group extension of a finite group $G$ by the trivial $G$-module $\mathbb Q$ is a semidirect product

Published on 18 Apr 2026 - 13:01

1.3k

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Equivalent Conditions of Split Extension of Groups

Published on 25 Mar 2026 - 3:01

115

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Extension of surface group by cyclic is residually finite

Published on 25 Mar 2026 - 1:16

46

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Automorphisms and Extensions of Cyclic Groups

Published on 25 Mar 2026 - 3:07

61

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Given $\Bbb ZQ$-module $K$, how to construct $\theta:Q\to\text{Aut}(K)$?

Published on 25 Mar 2026 - 3:00

124

Views

The relation between group extension and factor set

Published on 27 Mar 2026 - 12:20

235

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The number of groups $G$ (up to isomorphism) such that $G/\mathbb{Z}_3\cong D_{2n}$

Published on 25 Mar 2026 - 6:06

List Question

Cup Products and Group Extensions

Functoriality of Lyndon-Hochschild-Serre spectral sequences in coefficients.

The extension of a connected, simply-connected Lie group by $\mathbb{Z}$ is trivial.

On the central extension of a group

Isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent

Find isomorphic extensions of $\mathbb Z_3$ by $\mathbb Z_3 \times \mathbb Z_3$ which are not equivalent

Extension that split for all p-Sylow

Is there always a way to break a group?

Showing that any central group extension of a finite group $G$ by the trivial $G$-module $\mathbb Q$ is a semidirect product

Equivalent Conditions of Split Extension of Groups

Extension of surface group by cyclic is residually finite

Automorphisms and Extensions of Cyclic Groups

Given $\Bbb ZQ$-module $K$, how to construct $\theta:Q\to\text{Aut}(K)$?

The relation between group extension and factor set

The number of groups $G$ (up to isomorphism) such that $G/\mathbb{Z}_3\cong D_{2n}$

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