A Remark on Groups with Trivial Multiplicator

Abstract

1. Ler Hn (G) denote the nth homology group of G (with trivial integral coefficients), The (Schur) multiplicator of G is then, by definition, H2(G). The object of this note is to construct infinitely many 4-generator groups which are not finitely related but have trivial multiplicator. These examples should be compared with the first ones given in [1] and [2]. The basic idea of the construction is the use of a Mayer-Vietoris sequence, in a manner which is very similar to that adopted by Stallings in [3], but with a different end in view. Thus our procedure here is in direct contrast to that followed in [1] and [2].