Complementability criterion of periodical almost soluble subgroups in the group containing it - Chernikov , S. N.; Chernikov , N. S. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
It is proved that if every prime Sylow subgroup of a periodic almost solvable (more generally, periodic W0-) subgroup H of a group G has a complement in G and if, moreover, H is at most countable and the set π(H) is finite, the subgroup H itself possesses a complement in G.