ON THE TYPESET OF A BUTLER B(2)-GROUP CLORINDA DE VIVO AND CLAUDIA METELLI

Abstract. A Butler B(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 decomposability 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 of the first kind, and study the rank of the group G() of elements of G with type