Geodesic
Generation of Local Integral Orthogonal Groups in Characteristic 2
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1178-1191

Voir la notice de l'article provenant de la source Cambridge University Press

In two previous papers (see 4; 5) O. T. O'Meara and I investigated the problem of generating the integral orthogonal group of a quadratic form by symmetries in the case where the underlying ring of integers was the integers of a dyadic local field of characteristic not 2. In this paper, the investigation is concerned with a local field of characteristic 2. As in (5), only the unimodular case is treated. As in (4) and (5), groups S(L), Xh (L), and O(L) are introduced for a unimodular lattice L and the relationship between S(L) and O(L) studied. As in the previously cited papers, generation by symmetries means that S(L) = O(L). The following result is obtained. 
Pollak, Barth. Generation of Local Integral Orthogonal Groups in Characteristic 2. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1178-1191. doi: 10.4153/CJM-1968-112-9
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[1] 1. Arf, C., Untersuchungen iiber quadratischen Formen in Korpern der Charakteristik 2, J. Reine Angew. Math. 183 (1940), 148–167. Google Scholar

[2] 2. Chevalley, C., The algebraic theory of spinors (Columbia Univ. Press, New York, 1954).10.7312/chev93056 Google Scholar | DOI

[3] 3. Dieudonné, J., Sur les groupes classiques (Hermann, Paris, 1948). Google Scholar

[4] 4. O'Meara, O. T. and Pollak, Barth, Generation of local integral orthogonal groups, Math. Z. 87 (1965), 385–400. Google Scholar

[5] 5. O'Meara, O. T. and Pollak, Barth, Generation of local integral orthogonal groups. II, Math. Z. 93 (1966), 171–188. Google Scholar

[6] 6. Riehm, C. R., Integral representations of quadratic forms in characteristic 2, Amer. J. Math. 87 (1965), 32–64. Google Scholar

[7] 7. Sah, Chih-Han, Quadratic forms over fields of characteristic 2, Amer. J. Math. 82 (1960), 812–830. Google Scholar

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