Complementability criterion of periodical almost soluble subgroups in the group containing it

• Date: 1992
• Main Authors: Chernikov , S. N., Chernikov , N. S., Черников , С. Н., Черников , Н. С.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8016
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.