Abstract:A $B(2)$-group is a sum of a finite number of torsionfree Abelian groups of rank $1$, subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.
Keywords: Abelian group, torsionfree, finite rank, Butler group, $B(1)$-group, $B(2)$-group, type, tent, base change, direct decomposition, typeset
AMS Subject Classification: 20K15 06F99 06B99