List questions from group-extensions

Published on 24 Mar 2020 - 6:15

85

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Extensions of $A_5$ by $C_2$.

Published on 27 Mar 2020 - 16:52

48

Views

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

Published on 13 Apr 2020 - 23:18

63

Views

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

Published on 16 Mar 2026 - 7:45

115

Views

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

Published on 24 Apr 2020 - 9:46

122

Views

Is group extension unique?

Published on 27 Apr 2020 - 15:54

347

Views

Extensions of $A_5$ by $C_2$

Published on 02 May 2020 - 18:03

113

Views

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

Published on 04 May 2020 - 8:19

47

Views

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

Published on 05 May 2020 - 17:11

71

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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 07 May 2020 - 19:51

233

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 11 May 2020 - 3:45

44

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Extension-algebras of $A_4$

Published on 25 Mar 2026 - 4:40

411

Views

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

Published on 19 May 2020 - 3:08

99

Views

Centraliser in a group extension

Published on 24 May 2020 - 10:40

81

Views

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

Published on 25 May 2020 - 15:04

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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