Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T07:47:21.965Z Has data issue: false hasContentIssue false
  • English
  • Français

Generation of Local Integral Orthogonal Groups in Characteristic 2

Published online by Cambridge University Press:  20 November 2018

Barth Pollak
Barth Pollak*
Affiliation:
University of Notre Dame, Notre Dame, Indiana
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1178 - 1191
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This work was supported in part by the National Science Foundation under grant GP-3986.

References

1. Arf, C., Untersuchungen iiber quadratischen Formen in Korpern der Charakteristik 2, J. Reine Angew. Math. 183 (1940), 148–167.Google Scholar
2. Chevalley, C., The algebraic theory of spinors (Columbia Univ. Press, New York, 1954).10.7312/chev93056CrossRefGoogle Scholar
3. Dieudonné, J., Sur les groupes classiques (Hermann, Paris, 1948).Google Scholar
4. O'Meara, O. T. and Pollak, Barth, Generation of local integral orthogonal groups, Math. Z. 87 (1965), 385–400.Google Scholar
5. O'Meara, O. T. and Pollak, Barth, Generation of local integral orthogonal groups. II, Math. Z. 93 (1966), 171–188.Google Scholar
6. Riehm, C. R., Integral representations of quadratic forms in characteristic 2, Amer. J. Math. 87 (1965), 32–64.Google Scholar
7. Sah, Chih-Han, Quadratic forms over fields of characteristic 2, Amer. J. Math. 82 (1960), 812–830.Google Scholar