Abstract:
The author shows: the class of all periodic non-locally finite and non-locally nilpotent $FNN$-groups is non-empty and wide; an arbitrary binary graded $\overline{IH}$-group is solvable. At the same time, the author solves three natural S. N. Chernikov's questions. Also the author establishes that a non-Chernikov non-abelian group with normal such subgroups is solvable iff it is binary graded.
Keywords:an $FNN$-group, a locally nilpotent group, a locally finite group, a locally graded group, a binary graded group.
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