Covering a semi-direct product and intersective polynomials

Covering a semi-direct product and intersective polynomials

For a certain semi-direct product, we construct a 3-cover, consisting of three subgroups, the union of whose conjugates equals the whole group, while the intersection of the conjugates is trivial. This enables a classification of a new family of intersective polynomials. These polynomials have no ra...

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Veröffentlicht in:Manuscripta mathematica 2016-07, Vol.150 (3-4), p.521-531
Hauptverfasser: Lee, Paul D., Spearman, Blair K., Yang, Qiduan
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Zusammenfassung:For a certain semi-direct product, we construct a 3-cover, consisting of three subgroups, the union of whose conjugates equals the whole group, while the intersection of the conjugates is trivial. This enables a classification of a new family of intersective polynomials. These polynomials have no rational root but do have a root modulo every positive integer.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-015-0811-1