On groups with many nearly maximal subgroups

Franciosi, Silvana, and de Giovanni, Francesco. "On groups with many nearly maximal subgroups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.1 (1998): 19-23. <http://eudml.org/doc/252371>.

@article{Franciosi1998,
abstract = {A subgroup \( M \) of a group \( G \) is nearly maximal if the index \( |G : M | \) is infinite but every subgroup of \( G \) properly containing \( M \) has finite index, and the group \( G \) is called nearly \( IM \) if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly \( IM \) if and only if it is either cyclic or dihedral.},
author = {Franciosi, Silvana, de Giovanni, Francesco},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Nearly maximal subgroup; Nearly IM-group; Soluble group; nearly maximal subgroups; subgroups of infinite index; subgroups of finite index; intersections of maximal subgroups; nearly IM-groups},
language = {eng},
month = {3},
number = {1},
pages = {19-23},
publisher = {Accademia Nazionale dei Lincei},
title = {On groups with many nearly maximal subgroups},
url = {http://eudml.org/doc/252371},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Franciosi, Silvana
AU - de Giovanni, Francesco
TI - On groups with many nearly maximal subgroups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/3//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 1
SP - 19
EP - 23
AB - A subgroup \( M \) of a group \( G \) is nearly maximal if the index \( |G : M | \) is infinite but every subgroup of \( G \) properly containing \( M \) has finite index, and the group \( G \) is called nearly \( IM \) if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly \( IM \) if and only if it is either cyclic or dihedral.
LA - eng
KW - Nearly maximal subgroup; Nearly IM-group; Soluble group; nearly maximal subgroups; subgroups of infinite index; subgroups of finite index; intersections of maximal subgroups; nearly IM-groups
UR - http://eudml.org/doc/252371
ER -