Automorphism groups of endomorphism semigroups of free periodic groups

TL;DR

This paper characterizes the automorphism groups of endomorphism semigroups of free Burnside groups, establishing their isomorphism with automorphism groups of the groups themselves, for large odd exponents.

Contribution

It proves that the automorphism group of the endomorphism semigroup of free Burnside groups is isomorphic to the automorphism group of the groups, revealing a structural equivalence.

Findings

Aut(End(B(m,n))) is isomorphic to Aut(B(m,n))

Isomorphism of automorphism groups implies equal m

Results hold for odd exponents n ≥ 1003

Abstract

In this paper we describe the automorphism groups of the endomorphism semigroups of free Burnside groups $B(m,n)$ for odd exponents $n\ge1003$. We prove, that the groups $Aut(End(B(m,n)))$ and $Aut(B(m,n))$ are isomorphic. In particular, if the groups $Aut(End(B(m,n)))$ and $Aut(End(B(k,n)))$ are isomorphic, then $m=k$.