Non-cancellation Phenomena in the Class Of Finitely Generated Groups with Finite Commutator Subgroups

Abstract

We observe some non-cancellation phenomena arising from recent studies of the non-cancellation set χ (G) of a certain group G. Here χ (G) denotes the set of all isomorphism classes of groups H such that H × Z G × Z. In particular, there is a group structure on the set χ (G), and we compare this group operation with direct product formation. We also study a particular class of groups for which the non-cancellation set is trivial.