Invariable generation does not pass to finite index subgroups
Group Theory
2020-06-11 v1
Abstract
Using small cancellation methods, we show that the property invariable generation does not pass to finite index subgroups, answering questions of Wiegold and Kantor-Lubotzky-Shalev. We further show that a finitely generated group that is invariably generated is not necessarily finitely invariably generated, answering a question of Cox. The same results were also obtained independently by Minasyan.
Keywords
Cite
@article{arxiv.2006.05523,
title = {Invariable generation does not pass to finite index subgroups},
author = {Gil Goffer and Nir Lazarovich},
journal= {arXiv preprint arXiv:2006.05523},
year = {2020}
}