Abstract
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.
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Lee, P.D., Spearman, B.K. & Yang, Q. Covering a semi-direct product and intersective polynomials. manuscripta math. 150, 521–531 (2016). https://doi.org/10.1007/s00229-015-0811-1
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DOI: https://doi.org/10.1007/s00229-015-0811-1