Sugli S2 gruppi finiti

Abstract Let S group propertie of supersolvability. In this paper, with reference to finite case alone, we determine the simple S 2 -groups and characterize the non solvable S 2 -groups; we investigate furthermore the Sylow properties of solvable S 2 -groups

Pure B(n)-subgroups of completely decomposable groups

Abstract. We show a simple way to determine purity for a B(n)-group contained in a completely decomposable group

On direct sums of B(1)-groups--II

Abstract. B(1)-groups are a class of torsionfree Abelian groups of finite rank, part of the main class of Butler groups. In the paper C. Metelli, On direct sums of B(1)-groups, Comment. Math. Univ. Carolinae 34 (1993), 587–591, the problem of direct sums of B(1)-groups was discussed, and a necessary and sufficient condition was given for the direct sum of two B(1)-groups to be a B(1)-group. While sufficiency holds, necessity was wrongly claimed; we solve here the problem, and in the process study a curious hierarchy among indecomposable direct summands of B(1)-groups

Finite partition lattices and Butler groups

Abstract We investigate a special relation between finite partition lattices and distributive lattices. This will allow us to explore the close relationship between a class of torsionfree Abelian groups (the subclass of the class of Butler groups consisting of B (1) - groups) and a category of order-preserving morphisms mapping partition lattices into distributive lattices