Exterior and Symmetric Powers of Modules for Cyclic 2-Groups

TL;DR

This paper introduces a recursive formula for computing exterior and symmetric powers of modules over cyclic 2-groups, simplifying calculations and extending known results beyond prime order cyclic groups.

Contribution

It provides the first recursive method for these powers in cyclic 2-groups, generalizing previous prime order results.

Findings

Recursive formula for exterior powers

Recursive formula for symmetric powers

Simplified computation process

Abstract

We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.