Structure of the infinite Sylov subgroup in some Shunkov groups

The author studies groups entered by V. P. Shunkov in 1975 and named in his honor Shunkov groups in 2000, for the study the author uses a technique of infinite groups, developed at Krasnoyarsk School on group theory. The aim of the work was to establish the structure of an infinite Sylov 2-subgroup in Shunkov that does not have an almost layer-finite periodic part, when the normalizer of any finite non-trivial subgroup has an almost layer-finite periodic part. The author proves that if a Sylov 2-subgroup of the group is infinite, then it is an extension of a quasi-cyclic 2-group by reversing automorphism. This result will be used in the study of infinite groups with finiteness conditions. The structure of the unknown infinite Sylov 2-subgroup was completely revealed.