Self-normalizing nilpotent subgroups of the full linear group over a finite field

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1981 English Publisher:Springer Science and Business Media LLCJournal:Journal of Soviet Mathematics, volume 17, pages 1,963-1,967 (issn: 0090-4104, eissn: 1573-8795,

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Authors: Vavilov, N. A.;

doi: 10.1007/bf01465453

Self-normalizing nilpotent subgroups of the full linear group over a finite field

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Abstract

It has been proved (Ref. Zh. Mat., 1977, 4A170) that in the full linear group GL(n,q), n=2, 3, over a finite field of q elements, q odd or q=2, the only self-normalizing nilpotent subgroups are the normalizers of Sylow 2-subgroups and that for even q>2 there are no such subgroups. In the present note it is deduced from results of D. A. Suprunenko and R. F. Apatenok (Re. Zh. Mat., 1960, 13586; 1962, 9A150) that this is true for any n.

Keywords

Linear algebraic groups over finite fields, Other matrix groups over fields, Sylow 2-subgroups, self-normalizing nilpotent subgroups

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