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A Theorem on Permutations of a Finite Field

Published online by Cambridge University Press:  20 November 2018

A. Bruen  and
B. Levinger
A. Bruen
Affiliation:
University of Western Ontario, London, Ontario
B. Levinger
Affiliation:
Colorado State University, Fort Collins, Colorado
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The purpose of this note is to give a new proof of a theorem of L. Carlitz [2] and R. McConnel [5]. The theorem is as follows:

THEOREM 1. Let F = GF(pn) be the finite field of order q = pn and let K — {x ∈ F|xd = 1} for some proper divisor d of q — 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1060 - 1065
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bruen, A., Permutation functions on a finite field, Can. Math. Bull. 15 (1972), 595–597.Google Scholar
2. Carlitz, L., A theorem on permutations in a finite field, Proc. Amer. Math. Soc. 11 (1960), 456–59.Google Scholar
3. Foulser, D. A., Replaceable translation nets, Proc. London Math. Soc. 22 (1971), 235–264.Google Scholar
4. Hall, M., Jr., The theory of groups (Macmillan, New York, 1959).Google Scholar
5. McConnel, R., Pseudo-ordered polynomials over a finite field, Acta Arith. 8 (1963), 127–151.Google Scholar
6. Ostrom, T. G., Vector spaces and construction of finite projective planes, Arch. Math. (Basel) 19 (1968), 1–25.Google Scholar
7. Passman, D. S., Permutation groups (Benjamin, New York, 1968).Google Scholar
8. Wielandt, H. W., Finite permutation groups (Academic Press, New York, 1964).Google Scholar
9. Wielandt, H. W., Permutation groups through invariant relations and invariant functions, Lecture notes, Columbus, Ohio State University, 1969.Google Scholar