Some notes on the Baer-invariant of a nilpotent product of groups

Abstract

W. Haebich (1972, Bull. Austral. Math. Soc. 7, 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. © 2001 Academic Press.