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Abelian Unipotent Subgroups of Finite Unitary and Symplectic Groups

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  09 April 2009

W. J. Wong
W. J. Wong
Affiliation:
Department of Mathematics University of Notre DameNotre Dame, Indiana 46556, U.S.A.
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Abstract

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If G is the unitary group U(V) or the symplectic group Sp(V) of a vector space V over a finite field of characteristic p, and r is a positive integer, we determine the abelian p-subgroups of largest order in G whose fixed subspaces in V have dimension at least r, with the restriction that we assume p ≠ 2 in the symplectic case. In particular, we determine the abelian subgroups of largest order in a Sylow p-subgroup of G. Our results complement earlier work on general linear and orthogonal groups.

MSC classification

Secondary: 20G40: Linear algebraic groups over finite fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 331 - 344
Copyright
Copyright © Australian Mathematical Society 1982

References

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