Representations of Finite Polyadic Groups

TL;DR

This paper establishes a correspondence between irreducible representations of finite polyadic groups and their Post's cover, extending classical character theory results from groups to polyadic groups.

Contribution

It introduces a novel correspondence linking polyadic group representations to their Post's cover and generalizes key properties of irreducible characters to polyadic groups.

Findings

One-to-one correspondence between irreducible representations and Post's cover.

Generalization of properties of irreducible characters to polyadic groups.

Extension of classical representation theory results.

Abstract

We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite groups to the case of polyadic groups.