A class of Butler groups and their endomorphism rings

Abstract

We study a class of Butler groups of infinite rank, called Hawaiian groups.They are defined as subgroups of a rational vector space and contain parameters that provide for flexibility but are concrete enough to allow for the computation of certain crucial subgroups and quotient groups, to exhibit endomorphisms and describe the endomorphism rings. Most Hawaiian groups are finitely Butler; under stronger assumptions they are not finitely filtered and hence not $B_2$-groups.