Almost layer-finiteness of the periodic part of a group without involutions

We prove the following theorem which characterises the class of groups without involutions which have an almost layer-finite periodic part: if the normaliser of any non-trivial finite subgroup of a Shunkov group without involutions has an almost layer-finite periodic part, then the group also has an almost layer-finite periodic part.
The research was supported by the Russian Foundation for Basic Research, grant 99–01–00432, and by grant №9 of the 6th Competition of Scientific Projects of Young Researchers of Russian Academy of Sciences, 1999.