On Schur Multipliers of Pairs and Triples of Groups with Topological Approach

TL;DR

This paper explores the behavior of Schur multipliers in group pairs and triples using topological methods, relating them to homotopy pushouts and homology groups, and analyzing their properties under various group constructions.

Contribution

It introduces a topological approach to studying Schur multipliers of group pairs and triples, connecting them with homotopy pushouts and homology groups, and examines their behavior under different group operations.

Findings

Schur multipliers of pairs and triples relate to homotopy pushouts and homology groups.

Behavior of Schur multipliers under free, amalgamated free, and direct products.

Analysis of Schur multipliers in direct limits using topological methods.

Abstract

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits with topological approach.