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5.1 (1976)

Partially Solved

a) Is every locally finite minimal non-$FC$-group non-simple?
b) Is every locally finite minimal non-$FC$-group distinct from its derived subgroup? The question has an affirmative answer for minimal non-$BFC$-groups.

Contributor: V. V. Belyaev, N. F. Sesekin

Progress

a) Yes, it is (M. Kuzucuoğlu, R. E. Phillips, Proc. Cambridge Philos. Soc., 105, no. 3 (1989), 417–420).

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