Idempotent deformations of finite groups

TL;DR

This paper explores how idempotent deformations act on finite groups, analyzing their effects through homological properties and classifying the orbits of finite simple groups.

Contribution

It introduces a new framework for understanding idempotent deformations of finite groups via homological methods and classifies the orbits of finite simple groups under this action.

Findings

Orbits of finite simple groups are explicitly determined.

Homological properties characterize the action of deformations.

A new approach links deformations to group homology.

Abstract

The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.