The Unique Product Property of Groups and Their Amalgamated Free Products Original Research Article

A condition which can be used in establishing the unique product property for group coproducts with amalgamation is defined. This condition, called "vnn," has properties analogous to those of A. Lichtman′s inertia condition. Moreover, if K is both inert and vnn over H, then for any unique product group G containing H, the group L = K *H G is again a unique product group. Some examples of groups with subgroups exhibiting the vnn condition are given.