Class-Preserving Automorphisms of Generalized Free Products Amalgamating a Cyclic Normal Subgroup

Abstract

Abstract. In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every classpreserving automorphism of generalized free products of finitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than 8, is inner.

Class-preserving automorphisms of certain HNN extensions

“…Generalized free products of finitely generated nilpotent groups, amalgamating an infinite cyclic subgroup, have Property A [17]. However, there are generalized free products of finite nilpotent groups which do not have Property A [18]. In this direction, we are interested in conditions under which an HNN extension of a nilpotent group has Property A.…”