Published online by Cambridge University Press: 18 May 2009
In this paper, a problem of B. H. Neumann and Hanna Neumann [7] about the finite embeddability of an embeddable finite amalgam is discussed. After proving a “reduction theorem” for a finite amalgam to have a finite embedding, we examine some known embeddable amalgams (cf. [3]) as regards their embeddability in a finite group. Since the existence of the generalised free product and the embeddability of an amalgam are synonymous terms, Theorem 3.1 generalises a result in [4]. A sufficient condition for an amalgam of type S to have a finite embedding is also given.