Remarks to Glazek's results on n-ary groups

TL;DR

This paper surveys and extends results on the axiomatization, properties, and classifications of n-ary groups, including new findings, focusing on skew elements, homomorphisms, and covering group constructions.

Contribution

It provides a comprehensive survey of Glazek's work on n-ary groups with additional new results on their structure and properties.

Findings

New classifications of n-ary groups

Properties of skew elements analyzed

Constructions of covering groups developed

Abstract

It is a survey of the results obtained by K. Glazek's and his co-workers. We restrict our attention to the problems of axiomatizations of n-ary groups, classes of n-ary groups, properties of skew elements and homomorphisms induced by skew elements, constructions of covering groups, classifications and representations of n-ary groups. Some new results are added too.