Expansive dynamics on profinite groups

TL;DR

This paper characterizes profinite groups with expansive endomorphisms, showing they decompose into simple components like full one-sided group shifts and finite groups, revealing their restricted structure.

Contribution

It establishes a structural decomposition of profinite groups with expansive endomorphisms into fundamental components, linking group theory with symbolic dynamics.

Findings

Profinite groups with expansive endomorphisms are structurally restricted.

Such groups can be decomposed into finite sequences of full one-sided group shifts and finite groups.

The work connects algebraic properties with dynamical systems concepts.

Abstract

A profinite group equipped with an expansive endomorphism is equivalent to a one-sided group shift. We show that these groups have a very restricted structure. More precisely, we show that any such group can be decomposed into a finite sequence of full one-sided group shifts and two finite groups.