On the equationally Artinian groups

TL;DR

This paper investigates the property of being equationally Artinian in groups, proving stability under finite extensions and certain quotients, thus expanding the class of known equationally Artinian groups.

Contribution

It establishes that finite extensions and specific quotients of equationally Artinian groups are also equationally Artinian, broadening understanding of this property.

Findings

Finite extensions of equationally Artinian groups remain equationally Artinian.

Quotients of groups of the form G[t] by certain normal subgroups are equationally Artinian.

Provides new examples of equationally Artinian groups.

Abstract

In this article, we study the property of being equationally Artinian in groups. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian group of the form $G[t]$ by a normal subgroup which is a finite union of radicals, is again equationally Artnian. This provides a large class of examples of equationally Artinian groups.