Abstract
We consider a group without infinite ascending chains of nilpotent subgroups and prove that if every two elements of some conjugacy class generates a nilpotent subgroup then the whole class also generates a nilpotent subgroup.
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Mamontov, A.S. An Analog of the Baer-Suzuki Theorem for Infinite Groups. Siberian Mathematical Journal 45, 327–330 (2004). https://doi.org/10.1023/B:SIMJ.0000021288.57892.c6
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DOI: https://doi.org/10.1023/B:SIMJ.0000021288.57892.c6