The geometry of the conjugacy problem in lamplighter groups

TL;DR

This paper explores the conjugacy problem in lamplighter groups, demonstrating that the conjugacy length function grows linearly, highlighting the influence of geometric properties on algebraic problems.

Contribution

It establishes that the conjugacy length function in lamplighter groups is linear, emphasizing the role of geometric structure in solving the conjugacy problem.

Findings

Conjugacy length function in lamplighter groups is linear.

Geometry significantly influences the conjugacy problem.

Provides new insights into the algebraic structure of lamplighter groups.

Abstract

In this note we investigate the conjugacy problem in lamplighter groups with particular interest in the role of their geometry. In particular we show that the conjugacy length function is linear.