Abstract
AbstractDue to Narkiewicz a field F has property (P) if for no polynomial $$f\in F[x]$$
f
∈
F
[
x
]
of degree at least two there is an infinite f-invariant subset of F. We present a new example of an algebraic extension of $${\mathbb {Q}}$$
Q
satisfying (P). This is the first example in which we can find points of arbitrarily small positive Weil-height. Moreover, we study the possibility of property (P) for the field generated by all symmetric Galois extensions of $${\mathbb {Q}}$$
Q
. In particular we prove that there are no infinite backward orbits of non linear polynomials in this field.
Funder
Universität Duisburg-Essen
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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