Finite groups with $L$-free lattices of subgroups

Abstract

Balanced and strongly balanced lattices were introduced in order to generalize the uniform dimension of modular lattices. A description of finite groups with strongly balanced subgroup lattices was given by the authors in (Colloq. Math. 82 (1999), 65–77) and strengthened by Schmidt in (Illinois J. Math. 47 (2003), 515–528). In this paper, a description of finite groups with dually strongly balanced subgroup lattices is given.