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Journal of the London Mathematical Society 1997 55(2):387-399; doi:10.1112/S0024610796004760
© 1997 by London Mathematical Society
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© The London Mathematical Society

Extremal Subgroups in Chevalley Groups

Christopher Parker and Peter Rowley

Department of Mathematics and Statistics, University of Birmingham Edgbaston, Birmingham B15 2TT
Department of Mathematics, University of Manchester Institute of Science and Technology PO Box 88, Manchester M60 1QD

Received 12 April 1996. Revision received 10 November 1996.

Throughout this paper G(k) denotes a Chevalley group of rank n defined over the field k, where n≥3. Let {Phi} be the root system associated with G(k) and let {Pi}={{alpha}1, {alpha}2, ..., {alpha}n} be a set of fundamental roots of {Phi}, with {Phi}+ being the set of positive roots of {Phi} with respect to {Pi}. For {alpha}isin{Pi} and {gamma}isin{Phi}+, let n{alpha}({gamma}) be the coefficient of {alpha} in the expression of {gamma} as a sum of fundamental roots; so {gamma}={sum}{alpha}isin{Pi}n{alpha}({gamma}){alpha}. Also we recall that ht({gamma}), the height of {gamma}, is given by ht({gamma})={sum}{alpha}isin{Pi}n{alpha}({gamma}). The highest root in {Phi}+ will be denoted by {rho}. We additionally assume that the Dynkin diagram of G(k) is connected.


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