On exponentiation, $p$-automata and HNN extensions of free abelian groups

TL;DR

This paper demonstrates that many HNN extensions of free abelian groups can be faithfully represented using finite $p$-automata, linking algebraic structures with automata theory.

Contribution

It establishes a broad class of HNN extensions of free abelian groups that admit faithful finite $p$-automaton representations, a novel connection between group theory and automata.

Findings

Wide class of HNN extensions of free abelian groups admit faithful finite $p$-automata representations

For every prime p, such representations exist for the studied class

Bridges the gap between algebraic group extensions and automata theory

Abstract

For every prime $p$ it is shown that a wide class of HNN extensions of free abelian groups admit faithful representation by finite $p$-automata.