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SUBGROUPS OF ALGEBRAIC GROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS

Published online by Cambridge University Press:  01 April 1997

JAN SAXL  and
GARY M. SEITZ
JAN SAXL
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, Cambridge CB2 1SB. E-mail: J.Saxl@dpmms.cam.ac.uk
GARY M. SEITZ
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403, USA. E-mail: seitz@math.uoregon.edu
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Abstract

Let G be a simple algebraic group over an algebraically closed field K of characteristic p with p[ges ]0. Then G contains finitely many conjugacy classes of unipotent elements. There is a unique class of unipotent elements of largest dimension – the class of regular unipotent elements; the centralizer of any such element is a unipotent group of dimension equal to the rank of G. For example, if G is the linear group SL (V) on the finite dimensional vector space V over K, then the regular unipotent elements are precisely the unipotent matrices consisting of a single Jordan block.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 370 - 386
Copyright
The London Mathematical Society 1997

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