Sylow theory of CC-groups
\(G\) is a CC-group if \(G/C_ G(x^ G)\) is a Chernikov group. Results on Sylow \(p\)-subgroups of CC-groups were obtained by \textit{J. Alcazar} and \textit{J. Otal} [J. Algebra 110, No. 2, 507--513 (1987; Zbl 0624.20026)]. Here Sylow \(\pi\)-subgroups, Sylow bases and Carter subgroups (self-normalizing locally nilpotent subgroups) of periodic locally soluble CC-groups are considered and local conjugacy theorems are proved. Finally a large number of conditions equivalent to the conjugacy of Carter subgroups are obtained. For example, the following are equivalent: (a) the Carter subgroups of \(G\) are conjugate, (b) \(G\) has countable many Carter subgroups (c) the Sylow bases of \(G\) are conjugate, (d) \(G\) is (locally nilpotent)-by-finite.
self-normalizing locally nilpotent subgroups
scientific article; zbMATH DE number 4214252