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On conjugacy in a Chevalley group of large Abelian subgroups of the unipotent subgroup

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Abstract

Let U be the unipotent subgroup of a Chevalley group over a finite field. The well-known problem about describing the set of “large” (of maximal order) Abelian subgroups in U of exceptional type is investigated. The description of normal large Abelian subgroups in U was established earlier. It is proved that each large Abelian subgroup from U is conjugate in the Chevalley group of type F 4 over a finite field of characteristic not equal to 2 to a normal subgroup in U. It is shown that for the groups U of type G 2 and 3 D 4 a similar conclusion is not true.

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Authors and Affiliations

  1. Siberian Federal University, Krasnoyarsk, Russia

    G. S. Suleimanova

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  1. G. S. Suleimanova
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Correspondence to G. S. Suleimanova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 7, pp. 205–216, 2009.

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Suleimanova, G.S. On conjugacy in a Chevalley group of large Abelian subgroups of the unipotent subgroup. J Math Sci 169, 696–704 (2010). https://doi.org/10.1007/s10958-010-0070-3

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