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arXiv · 2006.05523

Invariable generation does not pass to finite index subgroups

Gil Goffer·Nir Lazarovich
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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.

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Gil Goffer, Nir Lazarovich. 2020-06-09. Invariable generation does not pass to finite index subgroups. https://arxiv.org/abs/2006.05523

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