Finite groups with modular chains

@article{RolandSchmidt2013,
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.},
author = {Roland Schmidt},
journal = {Colloquium Mathematicae},
keywords = {finite groups; subgroup lattices of groups; finite nilpotent groups; lower semimodular lattices; modular chains},
language = {eng},
number = {2},
pages = {195-208},
title = {Finite groups with modular chains},
url = {http://eudml.org/doc/284154},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Roland Schmidt
TI - Finite groups with modular chains
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 2
SP - 195
EP - 208
AB - 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.
LA - eng
KW - finite groups; subgroup lattices of groups; finite nilpotent groups; lower semimodular lattices; modular chains
UR - http://eudml.org/doc/284154
ER -