Sylow 2-subgroups of the periodic groups saturated with finite simple groups (Q515491)

For a fixed natural number \(n\), let \(A\) be the set of finite simple groups of Lie type in odd characteristic and of Lie rank at most \(n\). Let \(B\) be any finite set of finite groups and \(M = A \cup B\). The authors prove that in a periodic group \(G\) all of whose finite subgroups are in \(M\), all \(2\)-subgroups are Chernikov groups. The paper uses a result due to \textit{V. P. Shunkov} [Algebra Logic 7, 66--69 (1970; Zbl 0223.20043)], which shows that a 2-group is a Chernikov group provided it contains a finite maximal elementary abelian subgroup, or an involution whose centralizer is a Chernikov group. For the convenience of the reader, the authors include a proof of this result.