Clorinda De Vivo

DECOMPOSING B (1)-GROUPS: AN ALGORITHM

ABSTRACT An explicit algorithm is given to build an inner direct decomposition of a -group into indecomposables.

Finite partition lattices and butler groups

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.

On vector spaces with distinguished subspaces and redundant base

Abstract Let V , W be finite dimensional vector spaces over a field K , each with n distinguished subspaces, with a dimension-preserving correspondence between intersections. When does this guarantee the existence of an isomorphism between V and W matching corresponding subspaces? The setting where it happens requires that the distinguished subspaces be generated by subsets of a given redundant base of the space; this gives rise to a (0,1)-incidence table called tent , an object which occurs in the study of Butler B (1)-groups.

A condition of indecomposability for Butler \mathrm B (n)-groups

We give a manageable sufficient condition for indecomposability of Butler

On direct decompositions of Butler B(2)-groups

\mathrm B (n)

Butler groups splitting over a base element

B(n)-groups, allowing the easy construction of a big family of indecomposable torsionfree Abelian groups of finite rank.

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

In the study of Abelian groups a relevant role is played by realization of rings as endomorphism rings; this entails building from the ring a group on which the ring will act. We solve here a similar problem: given a ℚ-matrix M in the suitable class, build from it the Butler B (1)-groups for which M is a base change. The building procedure we give is an algorithm, easy to perform by hand in one-digit ranks.