Groups with nearly modular subgroup lattice

@article{FrancescodeGiovanni2001,
abstract = {A subgroup H of a group G is nearly normal if it has finite index in its normal closure $H^\{G\}$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we study the structure of groups in which all subgroups are nearly modular, proving in particular that a locally graded group with this property has locally finite commutator subgroup.},
author = {Francesco de Giovanni, Carmela Musella},
journal = {Colloquium Mathematicae},
keywords = {subgroup lattices; nearly modular lattices; nearly normal subgroups; nearly modular subgroups; subgroups of finite index; elements of finite order; locally graded groups; locally finite groups; FC-groups},
language = {eng},
number = {1},
pages = {13-20},
title = {Groups with nearly modular subgroup lattice},
url = {http://eudml.org/doc/283600},
volume = {88},
year = {2001},
}

TY - JOUR
AU - Francesco de Giovanni
AU - Carmela Musella
TI - Groups with nearly modular subgroup lattice
JO - Colloquium Mathematicae
PY - 2001
VL - 88
IS - 1
SP - 13
EP - 20
AB - A subgroup H of a group G is nearly normal if it has finite index in its normal closure $H^{G}$. A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we study the structure of groups in which all subgroups are nearly modular, proving in particular that a locally graded group with this property has locally finite commutator subgroup.
LA - eng
KW - subgroup lattices; nearly modular lattices; nearly normal subgroups; nearly modular subgroups; subgroups of finite index; elements of finite order; locally graded groups; locally finite groups; FC-groups
UR - http://eudml.org/doc/283600
ER -