Almost regular involutory automorphisms of uniquely 2-divisible groups

TL;DR

This paper proves that if a uniquely 2-divisible group has an almost regular involutory automorphism, then the group must be solvable, revealing a structural property linked to such automorphisms.

Contribution

It establishes a new solvability criterion for uniquely 2-divisible groups based on the existence of an almost regular involutory automorphism.

Findings

Uniquely 2-divisible groups with such automorphisms are solvable.

The automorphism's properties impose strong structural constraints.

Provides insight into the symmetry and structure of these groups.

Abstract

We prove that a uniquely 2-divisible group that admits an almost regular involutory automorphism is solvable.