Axiomatisability of the Class of Monolithic Groups in a Variety of Nilpotent Groups

TL;DR

This paper proves that the class of subdirectly irreducible groups within a variety generated by a finite nilpotent group can be characterized by a finite set of elementary axioms.

Contribution

It establishes a finite axiomatization for a specific class of groups in a variety generated by finite nilpotent groups, advancing the understanding of their logical structure.

Findings

Finite axiomatization of subdirectly irreducible groups

Characterization within varieties generated by finite nilpotent groups

Elementary sentences suffice for axiomatization

Abstract

The class of all subdirectly irreducible groups belonging to a variety generated by a finite nilpotent group can be axiomatised by a finite set of elementary sentences.