Groups with Few Nonmodular Subgroups - De, Mari F. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
Let G be a Tarski-free group such that the join of all nonmodular subgroups of G is a proper subgroup in G. It is proved that G contains a finite normal subgroup N such that the quotient group G/N has a modular subgroup lattice.