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Involutions in Chevalley groups over fields of even order

Published online by Cambridge University Press:  22 January 2016

Michael Aschbacher
Affiliation:
California Institute of Technology, University of Oregon
Gary M. Seitz
Affiliation:
California Institute of Technology, University of Oregon
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Let G = G(q) be a Chevalley group defined over a field Fq of characteristic 2. In this paper we determine the conjugacy classes of involutions in Aut(G) and the centralizers of these involutions. This study was begun in the context of a different problem.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Aschbacher, M., Tightly embedded subgroups of finite groups, (to appear).Google Scholar
[2] Aschbacher, M., On finite groups of component type, III. J. Math., 19 (1975), 87115.Google Scholar
[3] Aschbacher, M. and Seitz, G., On groups with a standard component of known type, (to appear).Google Scholar
[4] Borel, A. and Tits, J., Éléments unipotents et sousgroupes paraboliques de groupes réductifs, I, Inventiones Math., 12 (1971), 95104.CrossRefGoogle Scholar
[5] Bourbaki, N., Groupes et algebres de Lie, Chap. 4, 5, 6 Fascicule XXXIV, Elements de Math., Paris, Hermann 1968.Google Scholar
[6] Carter, R., Simple groups of Lie type, Wiley, New York, 1972.Google Scholar
[7] Curtis, C. Kantor, W., and Seitz, G., The two transitive permutation representations of the finite Chevalley groups, Trans. A. M. S., 218 (1976), 159.Google Scholar
[8] Fendei, D., A characterization of Conway’s group, 3, J. Alg., 24 (1973), 159196.Google Scholar
[9] Feit, W., The current situation in the theory of finite simple groups, Actes. Congress Intern. Math., 1 (1974), 5593.Google Scholar
[10] Fong, P., and Seitz, G., Groups with a (B, N)-pair of rank 2, I, II, Inventiones Math., 21, 24 (1973), (1974), 157, 191239.Google Scholar
[11] Frame, J., The characters of the Weyl group of E8 , Computational Problems in Abstract Algebra, 111130, Pergamon Press, Oxford, (1970) (Ed. Leech, J.).Google Scholar
[12] Gorenstein, D., Finite Groups, Harper and Row, New York, 1968.Google Scholar
[13] Griess, R., Schur multipliers of the finite simple groups of Lie type (to appearGoogle Scholar
[13] Griess, R., Schur multipliers of the finite simple groups of Lie type, Trans. A. M. S., 183 (1973), 355421.CrossRefGoogle Scholar
[14] Guterman, , A characterization of the groups F4(2n), J. Alg., 20 (1972), 123.CrossRefGoogle Scholar
[15] Hamill, C., A collineation group of order 213 • 35 • 52 • 7, Proc. London Math. Soc., 3 (1953), 5479.Google Scholar
[16] Hunt, D., A characterization of the finite simple groups M (22), J. Alg., 21 (1972), 103112.Google Scholar
[17] Lang, S., Algebraic groups over finite field, Amer. J. Math., 18 (1956), 555563.Google Scholar
[18] Parrot, D., A characterization of the Ree groups 2F4(q), J. Alg., 27 (1973), 341357.Google Scholar
[19] Seitz, G., Flag-transitive subgroups of Chevalley groups, Annals of Math., 97 (1973), 2756.Google Scholar
[20] Seitz, G., and Wright, C., On complements of F-residuals in finite solvable groups, Archiv. der Math., 21 (1970), 139150.Google Scholar
[21] Steinberg, R., Automorphisms of finite linear groups, Canadian J. Math., 12 (1960), 606615.Google Scholar
[22] Suzuki, M., Characterizations of linear groups, Bull, A. M. S., 75 (1969), 10431091.Google Scholar
[23] Thomas, G., A characterization of the group G2(2n), J. Alg., 13 (1969), 87118.Google Scholar
[24] Thomas, G., A characterization of the Steinberg group D4 2(q3), q=2n , J. Alg., 14 (1970), 373385.CrossRefGoogle Scholar
[25] Wall, G., On the conjugacy classes in the unitary, symplectic, and orthogonal groups, J. Australian Math. Soc., 3 (1963), 162.Google Scholar