On Shunkov Groups with a strongly embedded subgroup

Infinite Shunkov groups with the following condition are studied: the normalizer of any finite nontrivial subgroup has an almost layer-finite periodic part. Under this condition, the almost layer-finiteness of the periodic part of a Shunkov group with a strongly embedded subgroup possessing a Chernikov almost layer-finite periodic part is established. Earlier, the author proved the almost layer-finiteness of a Shunkov group with a strongly embedded group under the conditions that all proper subgroups are almost layer-finite and that the group is periodic.