Generalized Covering Groups and Direct Limits

TL;DR

This paper extends the understanding of how generalized covering groups behave with respect to direct limits, showing they commute under certain conditions, which aids in analyzing complex group structures.

Contribution

It generalizes Schur's formula for $ ext{V}$-covering groups and demonstrates their structure commutes with direct limits, enabling broader applications.

Findings

$ ext{V}$-covering groups' structure commutes with direct limits

Extension of known $ ext{V}$-covering group structures to infinite families

Application to complex group product structures

Abstract

M. R. R. Moghaddam (Monatsh. Math. 90 (1980) 37-43.) showed that the Baer invariant commutes with the direct limit of a directed system of groups. In this paper, using the generalization of Schur's formula for the structure of a $\mathcal{V}$-covering group for a Schur-Baer variety $\mathcal{V}$, we show that the structure of a $\mathcal{V}$-covering group commutes with the direct limit of a directed system, in some senses. It has a useful application in order to extend some known structures of $\mathcal{V}$-covering groups for several famous products of finitely many to an arbitrary family of groups.