List questions from group-extensions

Published on 25 Mar 2026 - 12:31

87

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Extensions of $A_5$ by $C_2$.

Published on 11 May 2026 - 0:34

51

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Why can the homomorphism $\phi$ in semi-direct products only be varied by inner automorphisms upon changing the complement group?

Published on 12 Apr 2026 - 18:12

71

Views

Some clarifications required about the two extremes of general extensions (semi-direct products and central extensions)

Published on 06 May 2026 - 12:33

116

Views

Relating a 2-cocycle to specific section of a central extension

Published on 25 Mar 2026 - 12:33

124

Views

Is group extension unique?

Published on 10 May 2026 - 12:22

349

Views

Extensions of $A_5$ by $C_2$

Published on 11 May 2026 - 0:35

114

Views

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Published on 25 Mar 2026 - 12:34

50

Views

Is the direct product $H \times K$ necessarily a central extension of $H$ by $K$ or $K$ by $H$?

Published on 13 Apr 2026 - 12:12

72

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$A_5$ or the icosahedral group $I$ is not isomorphic to any subgroup of the binary icosahedral group $2I$

Published on 25 Mar 2026 - 12:35

234

Views

The only group $G$ with one $A$ and one $B$ as composition factors is $G = A\times B$ (where $A$ and $B$ are non-abelian, finite and simple)

Published on 25 Mar 2026 - 14:25

46

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Extension-algebras of $A_4$

Published on 10 May 2026 - 13:57

412

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For Every Representation of a Subgroup is there a Group such that the Group Representation is Irreducible?

Published on 25 Mar 2026 - 12:34

100

Views

Centraliser in a group extension

Published on 25 Mar 2026 - 12:30

86

Views

$M<K\rtimes H$ is a semidirect product?

Published on 17 Apr 2026 - 1:08

List Question

Is $Ext^1_{Lie-Gr}(\mathbb C, \mathbb C^*)=0$?

Extensions of $A_5$ by $C_2$.

Why can the homomorphism $\phi$ in semi-direct products only be varied by inner automorphisms upon changing the complement group?

Some clarifications required about the two extremes of general extensions (semi-direct products and central extensions)

Relating a 2-cocycle to specific section of a central extension

Is group extension unique?

Extensions of $A_5$ by $C_2$

Why does every $\varphi: K \to \mathrm{Out}(H)$ determine an unique extension of $H$ by $K$ when $Z(H) = 1$?

Is the direct product $H \times K$ necessarily a central extension of $H$ by $K$ or $K$ by $H$?

$A_5$ or the icosahedral group $I$ is not isomorphic to any subgroup of the binary icosahedral group $2I$

The only group $G$ with one $A$ and one $B$ as composition factors is $G = A\times B$ (where $A$ and $B$ are non-abelian, finite and simple)

Extension-algebras of $A_4$

For Every Representation of a Subgroup is there a Group such that the Group Representation is Irreducible?

Centraliser in a group extension

$M<K\rtimes H$ is a semidirect product?

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