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Generating triples of involutions for Lie-type groups over a finite field of odd characteristic. I. (English. Russian original) Zbl 0966.20007
Algebra Logic 36, No. 1, 46-59 (1997); translation from Algebra Logika 36, No. 1, 77-96 (1997).
[For part II see Algebra Logika 36, No. 4, 422-440 (1997; Zbl 0936.20008).]
Summary: It is proved that a simple Lie-type group $$G$$ of rank $$l\leq 4$$ over a field of odd characteristic is generated by three involutions of which two are commuting. As a consequence, the following result is obtained: $$G$$ is generated by two elements one of which is an involution and the order of the other is at most $$2h$$, where $$h$$ is the Coxeter number of a root system associated with $$G$$.

##### MSC:
 20D06 Simple groups: alternating groups and groups of Lie type 20F05 Generators, relations, and presentations of groups
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