On Baer Invariants of Triples of Groups

TL;DR

This paper extends the theory of Baer invariants to triples of groups, exploring their properties, behavior under direct limits, structure in free products, and conditions for torsion groups.

Contribution

It introduces the concept of Baer invariants for triples of groups and analyzes their properties, limits, and structural aspects in new contexts.

Findings

Baer invariants of triples preserve direct limits

Structure of nilpotent multiplier for free product triples

Conditions for Baer invariants to be torsion groups

Abstract

In this paper, we develop the theory of Baer invariants for triples of groups. First, we focus on the general properties of the Baer invariant of triples. Second, we prove that the Baer invariant of a triple preserves direct limits of directed systems of triples of groups. Moreover, we present a structure for the nilpotent multiplier of a triple of the free product in some cases. Finally, we give some conditions in which the Baer invariant of a triple is a torsion group.