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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 133–142
(Mi timm230)
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This article is cited in 9 scientific papers (total in 9 papers)
Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups
V. M. Levchuk, G. S. Suleimanova Institute of Mathematics, Siberian Federal University
Abstract:
The description of the automorphisms of an unipotent subgroup $U$ of a Chevalley group over a field $K$ known earlier for $\operatorname{char}K\ne2,3$ (Gibbs, 1970) was completed in 1990 together with a solution of problem (1.5) from A. S. Kondrat’ev's survey (Usp. Mat. Nauk, 1986). In the present paper, $\operatorname{Aut}U$ is described for the case of finitary Chevalley groups. For a Chevalley group of classical type, 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. Large Abelian normal subgroups were listed by the authors earlier.
Keywords:
finitary Chevalley group, unipotent subgroup, automorphism, large abelian subgroup.
Received: 19.01.2009
Citation:
V. M. Levchuk, G. S. Suleimanova, “Automorphisms and normal structure of unipotent subgroups of finitary Chevalley groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 133–142; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S118–S127
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https://www.mathnet.ru/eng/timm230 https://www.mathnet.ru/eng/timm/v15/i2/p133
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Abstract page: | 480 | Full-text PDF : | 141 | References: | 66 |
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