Hostname: page-component-77c89778f8-7drxs Total loading time: 0 Render date: 2024-07-19T07:39:20.909Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Barry, M. J. J. (1977), ‘Parabolic subgroups of groups of Lie type’, Ph.D. thesis, University of Notre Dame.Google Scholar
Barry, M. J. J. (1979), ‘Large abelian subgroups of Chevalley groups’, J. Austral. Math. Soc. Ser. A 27, 59–87.CrossRefGoogle Scholar
Barry, M. J. J. and Wong, W. J. (1982), ‘Abelian 2-subgroups of finite symplectic groups in characteristic 2’, J. Austral. Math. Soc. Ser. A.CrossRefGoogle Scholar
Dieudonné, J. (1955), La géométrie des groupes classiques (Springer-Verlag, Berlin).Google Scholar
Goozeff, J. T. (1970), ‘Abelian p-subgroups of the general linear group’, J. Austral. Math. Soc. 11, 257–259.CrossRefGoogle Scholar
Wong, W. J. (1981), ‘Abelian unipotent subgroups of finite orthogonal groups’, J. Austral. Math. Soc. Ser. A 32, 223–245.CrossRefGoogle Scholar