The structure of local integral orthogonal groups

James, D. G.

doi:10.1090/S0002-9947-1977-0435244-8

The structure of local integral orthogonal groups
HTML articles powered by AMS MathViewer

by D. G. James PDF

Trans. Amer. Math. Soc. 228 (1977), 165-186 Request permission

Abstract:

Let M be a lattice on a regular quadratic space over a nondyadic local field. The normal subgroups of the integral orthogonal group $O(M)$ are determined.

References

Ludwig Bröcker, Orthogonale Gruppen über diskret bewerteten vollständigen Körpern, Abh. Math. Sem. Univ. Hamburg 34 (1969/70), 238–251 (German). MR 268289, DOI 10.1007/BF02992466
D. G. James, On the structure of orthogonal groups over local rings, Amer. J. Math. 95 (1973), 255–265. MR 330316, DOI 10.2307/2373784
D. G. James, Orthogonal groups of three-dimensional anisotropic quadratic forms, J. Algebra 37 (1975), no. 1, 121–136. MR 392828, DOI 10.1016/0021-8693(75)90092-7
Robert Paul Johnson, Othogonal groups of local anisotropic spaces, Amer. J. Math. 91 (1969), 1077–1105. MR 257242, DOI 10.2307/2373317
Wilhelm Klingenberg, Orthogonale Gruppen über lokalen Ringen, Amer. J. Math. 83 (1961), 281–320 (German). MR 124414, DOI 10.2307/2372957
Kenneth E. Martin, Orthogonal groups over $\textbf {R}((\pi ))$, Amer. J. Math. 95 (1973), 59–79. MR 335658, DOI 10.2307/2373644

Introduction to quadratic forms

27

Barth Pollak, On the structure of local orthogonal groups, Amer. J. Math. 88 (1966), 763–780. MR 204530, DOI 10.2307/2373077
Barth Pollak, Orthogonal groups over $R((\pi ))$, Amer. J. Math. 90 (1968), 214–230. MR 223462, DOI 10.2307/2373433
Carl R. Riehm, Orthogonal groups over the integers of a local field. II, Amer. J. Math. 89 (1967), 549–577. MR 215930, DOI 10.2307/2373236
Carl Riehm, The congruence subgroup problem over local fields, Amer. J. Math. 92 (1970), 771–778. MR 268191, DOI 10.2307/2373373