Examples of locally finite groups

In this paper we construct examples of nonextremal locally finite groups for which every finite unsolvable subgroup is not embedded in any proper infinite subgroup. We also give an example of a locally finite simple group, any proper infinite subgroup of which is bigrade solvable.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 103–106, January, 1973.The author wishes to express his deep gratitude to Yu. M. Gorchakov for help and valuable advice in the preparation of the paper.