# Primitive monodromy group of polynomials

For a polynomial *f* in *C[X]*, let *G* be the Galois
group of the Galois closure of the field extension
*C(X)|C(f(X))*. We classify the groups *G* in the
indecomposable case. For polynomials with rational coefficients there
are, besides four infinite series, only three more ``sporadic"
examples. In the Appendix we reprove the classical Theorems of Ritt
about decompositions of polynomials using the group-theoretic setup.

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