Finite groups with modular chains
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 195-208
MSC: Primary 20D30; Secondary 06C10.
DOI: 10.4064/cm131-2-3
Abstract
In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.
