# Partial cohomology of groups and extensions of semilattices of abelian groups

## TL;DR

This paper extends the concept of partial cohomology to non-unital abelian groups and explores its applications in classifying extensions of semilattices of abelian groups by groups.

## Contribution

It introduces a generalized partial cohomology framework for non-unital groups and interprets low-dimensional cohomology in the context of semilattice extensions.

## Key findings

- Extended partial cohomology to non-unital cases
- Interpreted $H^1(G,A)$ and $H^2(G,A)$ in extension theory
- Provided new tools for classifying semilattice extensions

## Abstract

We extend the notion of a partial cohomology group $H^n(G,A)$ to the case of non-unital $A$ and find interpretations of $H^1(G,A)$ and $H^2(G,A)$ in the theory of extensions of semilattices of abelian groups by groups.