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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-3,
author = {Roland Schmidt},
title = {Finite groups with modular chains},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {195-208},
zbl = {1285.20022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-3}
}
Roland Schmidt. Finite groups with modular chains. Colloquium Mathematicae, Tome 131 (2013) pp. 195-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-2-3/