On the Automorphisms and Representations of Polyadic Groups

TL;DR

This paper provides a comprehensive method to describe automorphisms and representations of polyadic groups by relating them to their underlying binary group structures.

Contribution

It introduces a unified approach to determine automorphisms and representations of any polyadic group based on the automorphisms and representations of its associated binary group.

Findings

Complete description of automorphisms of polyadic groups

Complete description of representations of polyadic groups

Unified method applicable to arbitrary polyadic groups

Abstract

Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms and representations of $(G,f)$ in terms of automorphisms and representations of the binary group $(G, \cdot)$.