Abstract
It is a well known fact on Lorenz groups that a quadratic form f is definite if and only if the corresponding orthogonal group On(R∞, f) where R∞ is the real number field, is compact. In this note, we shall show that the analogue of this holds for the case of the p-adic orthogonal group On(Rp, f), where Rp is the rational p-adic number field, as a special result of the more general statement on the completely valued fields.
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