Butler groups and lattices of types
H. Pat Goeters, William Ullery · Czech digital mathematics library · 1990
Suppose T is a finite lattice of types and A is a completely decomposable finite rank torsion-free abelian group such that the type of each summand of A is an element of T. If G is a strongly indecomposable group of the form A/X, where X is a rank-1 pure subgroup of A, a sharp upper bound is determined for the rank of G in terms of lattice-theoretic properties of T.