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Large abelian subgroups of Chevalley groups

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  09 April 2009

Michael J. J. Barry
Michael J. J. Barry
Affiliation:
Department of MathematicsCarysfort CollegeBlackrock, Co. Dublin, Ireland.
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Abstract

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For any group S let Ab(S) = {A∣A is an abelian subgroup of S of maximal order}. Let G be a Chevalley group of type An, Bn, Cn, or Dn over a finite field of characteristic p and let. In this paper Ab(U) is determined for all such groups.

MSC classification

Secondary: 20G40: Linear algebraic groups over finite fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 59 - 87
Copyright
Copyright © Australian Mathematical Society 1979

References

Alperin, J. L. (1965), ‘Large abelian subgroups of p-groups’, Trans. Amer. Math. Soc. 117, 10–20.Google Scholar
Barry, M. J. J. (1977), Parabolic subgroups of groups of Lie type (doctoral dissertation submitted to the University of Notre Dame, Indiana).Google Scholar
Carter, R. W. (1972), Simple groups of Lie type (John Wiley and Sons, New York, 1972).Google Scholar
Goozeff, J. T. (1970), ‘Abelian p-subgroups of GL(n, p)’, J. Austral. Math. Soc. 11, 257–259.CrossRefGoogle Scholar
Humphreys, J. E. (1972), Introduction to Lie algebras and representation theory (Springer-Verlag, Berlin, 1972).CrossRefGoogle Scholar
Srinivasan, B. (1968), ‘The characters of the finite symplectic group Sp(4, q)’, Trans. Amer. Math. Soc. 131, 488–525.Google Scholar
Steinberg, R. (1959), ‘Variations on a theme of Chevalley’, Pacific J. Math. 9, 875–891.CrossRefGoogle Scholar
Steinberg, R. (1968), Lectures on Chevalley groups (Lecture notes (mimeo)), Yale University.Google Scholar
Thwaites, G. N. (1972), ‘The Abelian p-subgroups of GL(n, p) of maximal rank’, Bull. London. Math. Soc. 4, 313–320.CrossRefGoogle Scholar
Wong, W. J. (1969), ‘A characterization of the finite projective symplectic groups PSp (4, q)’, Trans. Amer. Math. Soc. 139, 1–35.Google Scholar