| Abstract: | It is proved that the group of spinor norms of autometries of a generalized quadratic lattice ℒ over the ring of integral
elements v
p
of a local field k
p
, in the case wherep∤2 and ℒ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries
of ℒ. As a corollary, an extension to the case of generalized quadratic lattices is given for known sufficient conditions
of coincidence of the genus and the spinor genus of a quadratic lattice. Bibliography: 9 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 161–173.
Translated by Yu. G. Teterin. |
