Cohomologies of finite abelian groups

TL;DR

This paper introduces a simplified resolution for computing the cohomology of finite abelian groups, enabling more efficient calculations for G-lattices and their duals.

Contribution

It presents a new simplified resolution method for trivial modules over finite abelian groups, improving upon standard resolutions.

Findings

Efficient computation of cohomologies for irreducible G-lattices.

Comparison shows the simplified resolution is more streamlined than standard methods.

Results facilitate better understanding of G-module structures.

Abstract

We construct a simplified resolution for the trivial G-module Z, where G is a finite abelian group, and compare it with the standard resolution. We use it to calculate cohomologies of irreducible G-lattices and their duals.