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Generation of classical groups. (English) Zbl 0832.20029
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. 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).

MSC:
20D06 Simple groups: alternating groups and groups of Lie type
20D05 Finite simple groups and their classification
20F05 Generators, relations, and presentations of groups
20G40 Linear algebraic groups over finite fields
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