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Polynomial cycles in finite extension fields. (English) Zbl 1028.11014
Let \(K/F\) be an algebraic field extension. The authors characterize finite orbits of polynomial mappings of \(K\) which are induced by polynomials over \(F\). As an application they determine all possible cycle lengths of such orbits in the case of a finite field \(F\).

11C08 Polynomials in number theory
11T06 Polynomials over finite fields
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