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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
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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

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