Abstract
Suppose that a locally finite group \(G\) has a 2-element \(g\) with Chernikov centralizer. It is proved that if the involution in \(\langle g\rangle \) has nilpotent centralizer, then \(G\) has a soluble subgroup of finite index.
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Communicated by J. S. Wilson.
To the memory of Brian Hartley (1939–1994).
The first author thanks CNPq-Brazil and the University of Brasilia for support and hospitality that he enjoyed during his visits to Brasilia.
N. Y. Makarenko was supported by the Russian Science Foundation, project no. 14-21-00065.
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Khukhro, E.I., Makarenko, N.Y. & Shumyatsky, P. Locally finite groups containing a \(2\)-element with Chernikov centralizer. Monatsh Math 179, 91–97 (2016). https://doi.org/10.1007/s00605-014-0701-8
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DOI: https://doi.org/10.1007/s00605-014-0701-8