On the typeset of a B(2)-group

Abstract. A ButlerB(2)-group G is a sum of finitely many torsionfree Abelian groups of rank 1, subject to two independent relations. In a paper appeared in the Volume in memory of A.L.S. Corner [DVM 12] we showed that the decom- posability of G depends on the occurrence of a certain type. We study here the types of G, determining which depend only on the two main structures of G - the base types and the basic partition - and which instead depend on the coefficients of the relations. We give an algorithm to compute the types σ of the first kind, and study the rank of the group G(σ) of elements of G with type ≥ σ.