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9.3 (1984)

Solved

Suppose that a countable locally finite group $G$ contains no proper subgroups isomorphic to $G$ itself and suppose that all Sylow subgroups of $G$ are finite. Does $G$ possess a non-trivial finite normal subgroup?

Contributor: V. V. Belyaev

Progress

Yes, it does (S. D. Bell, Černikov Sylow subgroups, (Ph. D. Thesis), University of Manchester, 1994).

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