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Generating Reflections For U(2, p2n). II, p = 2

Published online by Cambridge University Press:  20 November 2018

D. W. Crowe
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It is known [4] that the finite two- dimensional unitary group U(2, p2n) is generated by two reflections if p ≠ 2. The present note completes that result by giving two generating reflections for U(2, 22n), n > 1. As in [4] this implies that the points of the "unit circle " in the unitary plane over GF(22n), n > 1, are the vertices of a "regular unitary polygon" whose group of auto- 2n morphisms is U(2, 22n).

The final section gives abstract definitions for the particular groups U(2,24) and U(2,52) in terms of their generating reflections.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 213 - 217
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Albert, A.A., Fundamental concepts of higher algebra, Chicago, 1956.Google Scholar
2. Coxeter, H.S.M., The symmetry groups of the regular complex polygons, Arch, der Math. 13 (1962), 86–97.Google Scholar
3. Coxeter, H.S.M. and Moser, W.O.J., Generators and relations for discrete groups, Berlin-Gottingen- Heidelberg, 1957.Google Scholar
4. Crowe, D.W., Generating reflections for U(2,p2n), Proc. Amer. Math. Soc. 13 (1962), 500–502.Google Scholar
5. Shephard, G.C., Regular complex poly topes, Proc. Lond. Math. Soc. (3) 2 (1952), 82–97.Google Scholar