不变生成不传递给有限索引子群

Pub Date : 2020-06-09 DOI:10.4171/ggd/693

Gil Goffer, Nir Lazarovich

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引用次数: 4

摘要

利用小消去方法，我们证明了性质不变生成不传递给有限指数子群，回答了Wiegold和Kantor-Lubotzky-Shalev的问题。我们进一步证明了一个总是生成的有限生成群不一定是有限总是生成的，这回答了Cox的一个问题。Minasyan也独立获得了相同的结果。

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Invariable generation does not pass to finite index subgroups

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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