On the construction of permutation complexes for profinite groups

TL;DR

This paper discusses the construction of permutation complexes for profinite groups, specifically focusing on the Morava stabilizer group G_2 at prime 3, using homological algebra techniques.

Contribution

It introduces a method to construct permutation complexes for profinite groups leveraging homological algebra, expanding the toolkit for studying such groups.

Findings

Permutation complexes for G_2 constructed using homological algebra.

Provides a new approach to studying profinite groups.

Enhances understanding of the structure of Morava stabilizer groups.

Abstract

Goerss, Henn, Mahowald and Rezk construct a complex of permutation modules for the Morava stabilizer group G_2 at the prime 3. We describe how this can be done using techniques from homological algebra.