A note on groups of infinite rank whose proper subgroups are abelian-by-finite

Francesco de Giovanni, and Federica Saccomanno. "A note on groups of infinite rank whose proper subgroups are abelian-by-finite." Colloquium Mathematicae 137.2 (2014): 165-170. <http://eudml.org/doc/284063>.

@article{FrancescodeGiovanni2014,
abstract = {It is proved that if G is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of G are abelian-by-finite.},
author = {Francesco de Giovanni, Federica Saccomanno},
journal = {Colloquium Mathematicae},
keywords = {Abelian-by-finite groups; Prüfer rank; groups of infinite rank},
language = {eng},
number = {2},
pages = {165-170},
title = {A note on groups of infinite rank whose proper subgroups are abelian-by-finite},
url = {http://eudml.org/doc/284063},
volume = {137},
year = {2014},
}

TY - JOUR
AU - Francesco de Giovanni
AU - Federica Saccomanno
TI - A note on groups of infinite rank whose proper subgroups are abelian-by-finite
JO - Colloquium Mathematicae
PY - 2014
VL - 137
IS - 2
SP - 165
EP - 170
AB - It is proved that if G is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of G are abelian-by-finite.
LA - eng
KW - Abelian-by-finite groups; Prüfer rank; groups of infinite rank
UR - http://eudml.org/doc/284063
ER -