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Arithmetic of Orthogonal Groups (II)

Published online by Cambridge University Press:  22 January 2016

Takashi Ono
Takashi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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In [0], the writer proved some theorems of Hasse type for two orthogonal groups which operate on the same vector space. In this paper, we shall further generalize those results in two directions. One is to consider the propositions of that type for two orthogonal groups which operate respectively on two vector spaces whose dimensions are different from each other, and the other is to deal with some conspicuous subgroups of an orthogonal group simultaneously which play important roles in the structure theory for orthogonal groups. For this reason, the present paper consists of three steps §1, §2 and §3 which give the generalizations in the above sense of the results in the corresponding sections of [0].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 9 , October 1955 , pp. 129 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

[0] Ono, T., Arithmetic of Orthogonal Groups, J. Math. Soc. Japan, Vol. 7, No. 1, pp. 79–91, 1955.Google Scholar
[1] Dieudonné, J., Sur les groupes classiques, Actual. Sci. Ind., No. 1040, Paris (Hermann),. 1948.Google Scholar
[2] Dickson, L. E., Linear groups, Leipzing (Teubner), 1901.Google Scholar
[3] Dieudonné, J., On the automorphisms of the classical groups, Memoirs of the Amer. Math. Soc., Vol. 2, 1952.Google Scholar
[4] Witt, E., Theorie der quadratischen Formen in beliebigen Körpern, Crelles J., Bd. 176,. pp. 31–44, 1937.Google Scholar