Infinite groups of finite period.
A first, important, result of this paper is that there exist periodic groups containing elements of even order and only trivial normal \(2\)-subgroups, in which every pair of involutions generates a \(2\)-group. This proves that, in general, the Baer-Suzuki theorem cannot be extended to periodic groups and gives a negative answer to Question 11.11a in the \textit{Kourovka Notebook} [1990; Zbl 0748.20001]. As a consequence the authors point out examples of finite simple groups that are recognizable by spectrum in the class of finite groups but are not recognizable in the class of all groups. Reviewer's remark: In the English translation ``Baer-Suzuki theorem'' has become ``Baire-Suzuki theorem''.
scientific article; zbMATH DE number 6498559
scientific article