# On Free Polyadic Groups

## TL;DR

This paper characterizes when a polyadic group derived from a group G, automorphism G, and element b is free, providing a necessary and sufficient condition based on these components.

## Contribution

It introduces a precise criterion for the freeness of polyadic groups constructed from given groups, automorphisms, and elements.

## Key findings

- Provides a necessary and sufficient condition for freeness
- Links group properties with polyadic group structure
- Advances understanding of free polyadic groups

## Abstract

In this article, for a polyadic group(G,f),derived from group G by automorphism G and element b, we give a necessary and sufficient condition in terms of the group, the automorphism G, and the element b, in order that the polyadic group becomes free.