Subextensions for co-induced modules

TL;DR

This paper develops cohomological criteria for embedding group extensions with abelian kernels into split extensions of co-induced modules, generalizing previous results and analyzing conjugacy of complements.

Contribution

It introduces new cohomological conditions for embedding group extensions and explores conjugacy in split extensions of co-induced modules, extending prior work.

Findings

Established a criterion for embedding group extensions into split co-induced modules

Proved conjugacy conditions for complements in split extensions

Linked homomorphisms of cohomology groups to extension properties

Abstract

Using cohomological methods, we prove a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about the conjugacy of complements in split extensions of co-induced modules. Both results follow from a relation between homomorphisms of certain cohomology groups.