Using small cancellation methods, we show that invariable generation does not pass to finite index subgroups, answering questions of Wiegold (1977) and Kantor–Lubotzky–Shalev (2015). We further show that a finitely generated group that is invariably generated is not necessarily finitely invariably generated, answering a question of Cox (2021). The same results were also obtained independently by Minasyan (2021).
Classification :
20-XX
Mots-clés :
Invariably generated groups, small cancellation theory
Affiliations des auteurs :
Gil Goffer
1
;
Nir Lazarovich
2
1
Weizmann Institute of Science, Rehovot, Israel
2
Technion - Israel Institute of Technology, Haifa, Israel
Gil Goffer; Nir Lazarovich. Invariable generation does not pass to finite index subgroups. Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1267-1288. doi: 10.4171/ggd/693
@article{10_4171_ggd_693,
author = {Gil Goffer and Nir Lazarovich},
title = {Invariable generation does not pass to finite index subgroups},
journal = {Groups, geometry, and dynamics},
pages = {1267--1288},
year = {2022},
volume = {16},
number = {4},
doi = {10.4171/ggd/693},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/693/}
}
TY - JOUR
AU - Gil Goffer
AU - Nir Lazarovich
TI - Invariable generation does not pass to finite index subgroups
JO - Groups, geometry, and dynamics
PY - 2022
SP - 1267
EP - 1288
VL - 16
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/693/
DO - 10.4171/ggd/693
ID - 10_4171_ggd_693
ER -
%0 Journal Article
%A Gil Goffer
%A Nir Lazarovich
%T Invariable generation does not pass to finite index subgroups
%J Groups, geometry, and dynamics
%D 2022
%P 1267-1288
%V 16
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/693/
%R 10.4171/ggd/693
%F 10_4171_ggd_693
