Continuum varieties of groups and verbal embeddings of groups
by
Vahagn H. Mikaelian
Yerevan State University

In this talk we would like to show a few applications of the argument developed by Ol'shanskii for construction of continuum sets of varieties of groups to the concept of verbal embeddings of groups. The embedding j of the group H into the group G is verbal for the given word set V ⊆ F_∞ if the isomorphic copy j(H) lies in the verbal subgroup V(G). Using appropriately chosen groups H with appropriate word sets V we build continuum sets of soluble 3-generator non-Hopfian groups which are non-isomorphic and, moreover, generate pairwise distinct varieties of groups.

Date received: March 9, 2006