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Normalizers of subsystem subgroups in finite groups of Lie type. (Russian, English) Zbl 1155.20020

Algebra Logika 47, No. 1, 3-30 (2008); translation in Algebra Logic 47, No. 1, 1-17 (2008).
Summary: Finite groups of Lie type form the greater part of the known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of the subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing with the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem.

MSC:

20D25 Special subgroups (Frattini, Fitting, etc.)
20D06 Simple groups: alternating groups and groups of Lie type
20G40 Linear algebraic groups over finite fields
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