Co-prolongations of a group extension

TL;DR

This paper develops an obstruction theory for co-prolongations of central group extensions, classifying their equivalence classes via kernels of homomorphisms between second cohomology groups.

Contribution

It introduces a new framework for understanding co-prolongations of central extensions using cohomological methods and classifies them through homomorphisms between cohomology groups.

Findings

Constructed an obstruction theory for co-prolongations.

Classified equivalence classes via kernels of homomorphisms.

Linked co-prolongations to second cohomology group structures.

Abstract

The aim of this paper is to study co-prolongations of central extensions. We construct the obstruction theory for co-prolongations and classify the equivalence classes of these by kernels of a homomorphisms between 2-dimensional cohomology groups of groups.