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A Theorem on Permutations of a Finite Field

  • A. Bruen (a1) and B. Levinger (a2)

Extract

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.

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References

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1. Bruen, A., Permutation functions on a finite field, Can. Math. Bull. 15 (1972), 595597.
2. Carlitz, L., A theorem on permutations in a finite field, Proc. Amer. Math. Soc. 11 (1960), 456–59.
3. Foulser, D. A., Replaceable translation nets, Proc. London Math. Soc. 22 (1971), 235264.
4. Hall, M., Jr., The theory of groups (Macmillan, New York, 1959).
5. McConnel, R., Pseudo-ordered polynomials over a finite field, Acta Arith. 8 (1963), 127151.
6. Ostrom, T. G., Vector spaces and construction of finite projective planes, Arch. Math. (Basel) 19 (1968), 125.
7. Passman, D. S., Permutation groups (Benjamin, New York, 1968).
8. Wielandt, H. W., Finite permutation groups (Academic Press, New York, 1964).
9. Wielandt, H. W., Permutation groups through invariant relations and invariant functions, Lecture notes, Columbus, Ohio State University, 1969.
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A Theorem on Permutations of a Finite Field

  • A. Bruen (a1) and B. Levinger (a2)

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