Some Notes on the Baer Invariant of a Nilpotent Product of Groups

TL;DR

This paper investigates the Baer-invariant of nilpotent products of groups, providing new formulas and showing its relation to Haebich's earlier work on Schur multipliers, with specific focus on cyclic groups.

Contribution

It introduces formulas for the Baer-invariant of nilpotent products of groups, extending Haebich's results to this context and focusing on cyclic groups.

Findings

Baer-invariant has a homomorphic image and subgroup relation to Haebich's formula

Derived a specific formula for nilpotent products of cyclic groups

Established connections between Baer-invariant and Schur multiplier in this setting

Abstract

W.Haebich (Bull. Austral. Math. Soc., 7, 1972, 279-296) presented a formula for the Schur multiplier of a regular product of groups. In this paper first, it is shown that the Baer-invariant of a nilpotent product of groups with respect to the variety of nilpotent groups has a homomorphic image and in finite case a subgroup of Haebich's type. Second a formula will be presented for the Baer-invariant of a nilpotent product of cyclic groups with respect to the variety of nilpotent groups.