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The Automorphisms of the Group of Rotations and its Projective Group Corresponding to Quadratic Forms of any Index

Published online by Cambridge University Press:  20 November 2018

María J. Wonenburger
María J. Wonenburger*
Affiliation:
Queen's University
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Let M be a vector space of dimension n over a field K of characteristic ≠2 and f a non-degenerate quadratic form on M. The automorphisms of the orthogonal group On(K,f), the rotation group On+(K,f), and their corresponding projective groups POn(K,f), POn+(K,f), were determined by J. Dieudonné for n sufficiently large under the condition that the index of f is greater than zero (see 2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 302 - 303
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Artin, E., Geometric algebra (New York, 1957).Google Scholar
2. Dieudonné, J., On the automorphisms of the classical groups, Mem. Amer. Math. Soc, No. 2 (1951).Google Scholar
3. Dieudonné, J., La géométrie des groupes classiques (Berlin, 1955).Google Scholar
4. Rickart, C. E., Isomorphic groups of linear transformations I and II, Amer. J. Math., 72 (1950), 451–464, and 73 (1951), 697–716.Google Scholar
5. Walter, J. H., Isomorphisms between projective unitary -groups, Amer. J. Math., 77 (1955), 805–844.Google Scholar