Groups of the nilpotency class $3$ of order $p^4$ as additive groups of local nearrings

TL;DR

This paper investigates groups of nilpotency class 3 with order p^4 as additive groups of local nearrings, demonstrating the existence of such structures for primes greater than 3.

Contribution

It establishes the existence of local nearrings on certain nilpotent groups of order p^4 for primes p > 3, expanding understanding of nearring-group relationships.

Findings

Existence of local nearrings on specific nilpotent groups of order p^4 for p > 3

Identification of conditions under which these groups admit local nearrings

Contribution to the classification of groups as additive groups of local nearrings

Abstract

We consider groups of the nilpotency class $3$ of order $p^4$ which are the additive groups of local nearrings. It was shown that, for $p>3$, there exist a local nearring on one of such 4 groups.