Invariable generation does not pass to finite index subgroups

  • Gil Goffer

    Weizmann Institute of Science, Rehovot, Israel
  • Nir Lazarovich

    Technion - Israel Institute of Technology, Haifa, Israel
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Abstract

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).

Cite this article

Gil Goffer, Nir Lazarovich, Invariable generation does not pass to finite index subgroups. Groups Geom. Dyn. 16 (2022), no. 4, pp. 1267–1288

DOI 10.4171/GGD/693