Spinor norms of local autometries of generalized quadratic lattices

It is proved that the group of spinor norms of autometries of a generalized quadratic lattice $\mathcal L$ over the ring of integral elements $v_\mathfrak p$ of a local field $k_\mathfrak p$, in the case where $\mathfrak p\nmid2$ and $\mathcal L$ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries of $\mathcal L$. 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.