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Singer Groups

Published online by Cambridge University Press:  20 November 2018

Marshall D. Hestenes
Marshall D. Hestenes*
Affiliation:
Michigan State University, East Lansing, Michigan
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Interest in the Singer groups has arisen in various places. The name itself results from the connection Singer [7] made between these groups and perfect difference sets, and this is closely associated with the geometric property that a Singer group is regular on the points of a projective space. Some information about these groups appears in Huppert's book [3, p. 187]. Singer groups are frequently useful in constructing examples and counterexamples. Our aim in this paper is to make a systematic study of the Singer subgroups of the linear groups, with a particular view to analyzing the examples they provide of Frobenius regular groups. Frobenius regular groups are a class of permutation groups generalizing the Zassenhaus groups, and Keller [5] has shown recently that they provide a new characterization of A6 and M11.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 492 - 513
Copyright
Copyright © Canadian Mathematical Society 1970

References

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3. Huppert, B., Endliche Gruppen, Vol. I (Springer-Verlag, New York, 1967).Google Scholar
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7. Singer, J., A theorem infinite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43 (1938), 377–385.Google Scholar