On ${\cal N}_c$-Covering Groups of a Nilpotent Product of Cyclic Groups

TL;DR

This paper proves the existence and provides a structure for ${ m N}_c$-covering groups of nilpotent products of cyclic groups, advancing understanding of their algebraic properties.

Contribution

It establishes the existence of ${ m N}_c$-covering groups for nilpotent products of cyclic groups and describes their structure, building on previous work on Baer-invariants.

Findings

Existence of ${ m N}_c$-covering groups for nilpotent products of cyclic groups.

Structural description of these ${ m N}_c$-covering groups.

Extension of earlier Baer-invariant results to covering groups.

Abstract

The first author, in 2001, presented a structure for the Baer-invariant of a nilpotent product of cyclic groups with respect to the variety of nilpotent groups. In this paper, using the above structure, we prove the existence of an ${\cal N}_c$-covering group for a nilpotent product of a family of cyclic groups. We also present a structure for the ${\cal N}_c$-covering group.