논문KCI 등재
ON THE GALOIS GROUP OF ITERATE POLYNOMIALS
한국수학교육학회|2009.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제16권 제3호|pp. 283-296
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Let f(x) = xⁿ + a be a binomial polynomial in Z[x] and fm(x) be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of fm(x) is isomorphic to a wreath product group [Cn]m where Cn is a cyclic group of order n.
Abstract
Let f(x) = xⁿ + a be a binomial polynomial in Z[x] and fm(x) be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of fm(x) is isomorphic to a wreath product group [Cn]m where Cn is a cyclic group of order n.
참고문헌 (9)
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- L. Danielson, "The Galois theory of iterated binomials", 박사, pp.1995
- L. Danielson, "On the irreducibility of the iterates of xn ¡ b", Proc. Amer.Math. Soc, 130, pp.1589~1596 (2001)
- S. Lang, "Algebra. 3rd" (1993), Addison-Wesley
- R. W. K. Odoni, "The Galois theory of iterates and composites of polynomials", Proc.London Math. Soc, 51, pp.385~414 (1985)
- R. W. K. Odoni, "Realising wreath products of cyclic groups as Galois groups", Mathematika, 35, pp.101~113 (1988)
- H. E. Rose, "A course in number theory, 2nd ed" (1994), Oxford Science Publications
- M. Stoll, "Galois groups over Q of some iterated polynomials", Arch. Math, 59, pp.239~244 (1992)
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