An efficient algorithm for finding a basis of the fixed point subgroup of an automorphism of a free group

TL;DR

This paper presents an efficient algorithm to compute a basis for the fixed point subgroup of an automorphism in a free group, advancing computational methods in algebraic structures.

Contribution

It introduces a novel, efficient algorithm for finding bases of fixed point subgroups of automorphisms in free groups, improving on previous computational approaches.

Findings

Algorithm computes fixed point bases efficiently

Applicable to free groups of finite rank

Enhances computational algebra techniques

Abstract

We prove that for any automorphism $\alpha$ of a free group F of finite rank, one can efficiently compute a basis of the fixed point subgroup Fix(\alpha).