Vol. 106, No. 1, 1983

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The root subgroups for maximal tori in finite groups of Lie type

Gary Seitz

Vol. 106 (1983), No. 1, 153–244

Let G1 be a finite group of Lie type defined over a field of characteristic p. The results of this paper represent an attempt to achieve a better understanding of the subgroup structure of G1. It is somewhat surprising how limited our knowledge is, in this regard. For example, while centralizers of semisimple elements (i.e. p-elements) of G1 have been studied in detail and are fairly well understood, very little has been written about subgroups of G1 generated by such centralizers. Even in explicit examples the analysis of such subgroups can be very difficult, the difficulty stemming from an inability to relate the generated group to the Lie structure of G1. To deal with these situations and others we set up a framework that allows us to effectively study a fairly large class of subgroups of G1 (those containing a maximal torus), by studying subgroups of the corresponding algebraic group. Essential to the development is a theory of root subgroups for arbitrary maximal tori of G1.

Mathematical Subject Classification 2000
Primary: 20G40
Received: 21 July 1980
Published: 1 May 1983
Gary Seitz
University of Oregon
Eugene OR 97403
United States