Generation of classical groups
It is well known (modulo the classification of finite simple groups) that every finite group is generated by two elements and can not be generated by two involutions (= elements of order 2). The authors prove the following important Theorem A: every finite simple non-abelian group other than \(U_3(3)\) is generated by three involutions. \textit{A. Wagner} [Boll. Unione Mat. Ital., V. Ser., A 15, 431-439 (1978; Zbl 0401.20038)] has proved that \(U_3(3)\) can not be generated by any three of its involutions, but it is generated by four involutions. In fact, Theorem A has been proved previously for many series of simple groups; see the paper under review for references. Theorem B: every finite simple non- abelian group other than \(U_3(3)\) is generated by two elements, one of which is an involution and the other is a strongly real element (that is the product of two involutions).
scientific article; zbMATH DE number 553940
scientific article