Resumen de On the typeset of a Butler B(2)-group

Clorinda De Vivo, Claudia Metelli

• 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 which appeared in the Volume in memory of A.L.S. Corner (De Vivo, C. and Metelli, C., On direct decompositions of Butler B(2)-groups, Volume in memory of A.L.S. Corner, Contributions to Module Theory; Models, Modules and Abelian Groups, W. De-Gruyter (2008), 201-219) 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 s of the first kind, and study the rank of the group G(s) of elements of G with type =s.