Abstract
The description of the automorphisms of a unipotent subgroup U of a Chevalley group over a field K known earlier for charK ≠ 2, 3 (Gibbs, 1970) was completed in 1990 together with the solution of problem (1.5) from A.S. Kondrat’ev’s survey (Usp. Mat. Nauk, 1986). In the present paper, Aut U is described for the case of finitary Chevalley groups. For a Chevalley group of classical type over a finite field, it is proved that any large Abelian subgroup from U is conjugate to a normal subgroup in U. It is shown that this is not so in the general case; therefore, problem (1.6) from Kondrat’ev’s survey about large Abelian subgroups in U is reduced to listing the exceptions. The orders of these subgroups and large Abelian normal subgroups in U were listed earlier.
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Original Russian Text © V.M. Levchuk, G.S. Suleimanova, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 2.
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Levchuk, V.M., Suleimanova, G.S. Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups. Proc. Steklov Inst. Math. 267 (Suppl 1), 118–127 (2009). https://doi.org/10.1134/S0081543809070128
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DOI: https://doi.org/10.1134/S0081543809070128