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Automorphisms of Chevalley groups of types \(B_2\) and \(G_2\) over local rings. (English. Russian original) Zbl 1194.20049
J. Math. Sci., New York 155, No. 6, 795-814 (2008); translation from Fundam. Prikl. Mat. 13, No. 4, 3-29 (2007).
Let \(R\) be a local ring with a unit. In this paper, by generalizing some methods of V. M. Petechuk [Mat. Zametki 28, 187-204 (1980; Zbl 0437.20037)], consider every Chevalley group as embedded into the group \(\text{GL}_n(R)\) for some \(n\in\mathbb{N}\), and consider Chevalley groups as matrix groups, the author proves that every automorphism of any adjoint Chevalley group of type \(B_2\) or \(G_2\) is standard, i.e., it is a composition of an inner automorphism, a ring automorphism, and a central automorphism.

MSC:
20H25 Other matrix groups over rings
20E36 Automorphisms of infinite groups
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References:
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