Abstract
Many groups are best described as the group of automorphisms of some natural object. I’m interested in obtaining such descriptions of the finite simple groups, and more generally descriptions of the groups of Lie type over arbitrary fields. The representation of the alternating group of degree n as the group of automorphisms of a set of order n is an excellent example of such a description. The representation of the classical groups as the isometry groups of bilinear or sequilinear forms is another.
Partially supported by the National Science Foundation.
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References
R. Brown, Groups of type E7, J. fur die reine ang. Math. 236(1969), 79–102.
L. Dickson, Theory of linear groups in an arbitrary field, Trans. AMS 2(1901), 363–394.
L. Dickson, The configuration of 27 lines on a cubic surface and the 28 bitangents to a quartic curve, Bull. AMS 8(1901), 63–70.
L. Dickson, A class of groups in an arbitrary realm connected with the configuration of the 27 lines on a cubic surface, Quartly J. Math. 33(1901), 145–173.
E. Cartan, Oeuvres Completes, Gauthier-Vi11ars, Paris, 1952.
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© 1988 D. Reidel Publishing Company, Dordrecht, Holland
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Aschbacher, M. (1988). Some Multilinear Forms with Large Isometry Groups. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_15
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DOI: https://doi.org/10.1007/978-94-009-4017-8_15
Publisher Name: Springer, Dordrecht
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