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Galois Groups of Periodic Points

โœ Scribed by Patrick Morton


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
320 KB
Volume
201
Category
Article
ISSN
0021-8693

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Galois groups of irreducible trinomials X n + aX s + b โˆˆ X are investigated assuming the classification of finite simple groups. We show that under some simple yet general hypotheses bearing on the integers n s a and b only very specific groups can occur. For instance, if the two integers nb and as

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In this paper, we consider nonsplit Galois theoretical embedding problems with cyclic kernel of prime order p, in the case where the ground field has characteristic / p. It is shown that such an embedding problem can always be reduced to another embedding problem, in which the ground field contains

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We propose a conjecture on the distribution of number fields with given Galois group and bounded norm of the discriminant. This conjecture is known to hold for abelian groups. We give some evidence relating the general case to the composition formula for discriminants, give a heuristic argument in f

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Let f be a continuous map of an interval I/R. The periods of the periodic points of f are described by a theorem of Sarkovskii [6,12], which defines an ordering in the set N\* of all positive integers in such a way that if n # N\* is a period of x # I, every integer following n in Sarkovskii's order