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- W2108883344 abstract "Let $f,gin mathbb {Z}[X]$ be non-constant polynomials with integral coefficients. In 1968 H. Davenport raised the question as to when the value sets $f(mathbb {Z})$ and $g(mathbb {Z})$ are the same modulo all but finitely many primes. The main progress until now is M. Friedâs result that $f$ and $g$ then differ by a linear substitution, provided that $f$ is functionally indecomposable. We extend this result to polynomials $f$ of composition length $2$. Also, we study the analog when $mathbb {Z}$ is replaced by the integers of a number field. The above number theoretic property translates to an equivalent property of subgroups of a finite group, known as Kronecker conjugacy, a weakening of conjugacy which has been studied by various authors under different assumptions and in other contexts. We also give a simplified and strengthened version of the Galois theoretic translation to finite groups." @default.
- W2108883344 created "2016-06-24" @default.
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- W2108883344 date "1998-01-01" @default.
- W2108883344 modified "2023-09-26" @default.
- W2108883344 title "Kronecker conjugacy of polynomials" @default.
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- W2108883344 doi "https://doi.org/10.1090/s0002-9947-98-02123-0" @default.
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