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1Department of Mathematics, Imperial College, London, SW7 2AZ, U.K. E-mail: davis.stewart06@imperial.ac.uk and dis20@cantab.net
Citation Information: Journal of Group Theory. Volume 13, Issue 1, Pages 117–130, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/jgt.2009.035, July 2009
Let G ≔ G 2(K) be a simple algebraic group of type G 2 defined over an algebraically closed field K of characteristic p > 0. Let σ denote a standard Frobenius automorphism of G such that G σ ≅ G 2(q) with q ⩾ 4. In this paper we find all reductive subgroups of G and quasi-simple subgroups of G σ in the defining characteristic. Our results extend the complete reducibility results of [Liebeck and Seitz, Mem. Amer. Math. Soc. 121: 580, 1996, Theorem 1].
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