Spinor norms of local autometries of generalized quadratic lattices

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.