Abstract
We describe simple Lie-type groups of rank l≤3 over a finite field of odd characteristic, generated by three involutions of which two are commuting. Previously, the answers to the similar questions were given for alternating groups, for Lie-type groups over a finite field of characteristic 2, and for Lie-type groups of rank l≥4 over a finite field of odd characteristic. These furnish a description of finite simple non-Abelian groups, distinct from 26 sporadic groups, generated by three involutions two of which are commuting, thus giving a partial answer to question 7.30 posed by Mazurov in the Kourovka Notebook.
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Supported by RFFR grant No. 94-01-01084.
Translated from Algebra i Logika, Vol. 36, No. 4, pp. 422–440, July–August, 1997.
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Nuzhin, Y.N. Generating triples of involutions for lie-type groups over a finite field of odd characteristic. II. Algebr Logic 36, 245–256 (1997). https://doi.org/10.1007/s10469-997-0066-3
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DOI: https://doi.org/10.1007/s10469-997-0066-3