Polyadic groups and automorphisms of cyclic extensions

TL;DR

This paper explores the automorphism groups of n-ary groups and demonstrates how they can be embedded into automorphism groups of cyclic extensions, revealing new structural insights.

Contribution

It introduces a method to embed automorphism groups of n-ary groups into those of cyclic extensions, providing a novel approach to understanding their automorphisms.

Findings

Automorphism group of an n-ary group can be embedded into that of a cyclic extension.

Provides a new class of automorphisms for cyclic extensions.

Establishes structural relationships between n-ary groups and cyclic extensions.

Abstract

We show that for any $n$-ary group $(G,f)$, the group $Aut(G,f)$ can be embedded in $Aut(\mathbb{Z}_{n-1}\ltimes G)$ and so we can obtain a class of interesting automorphisms of cyclic extensions.