Mathematics – Group Theory
Scientific paper
2011-05-10
Mathematics
Group Theory
29 pages
Scientific paper
A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each conjugacy class is big enough. The result is applied to the problem on the number of irreducible components of the Hurwitz space of degree $d$ marked coverings of $\mathbb P^1$ with given Galois group $G$ and fixed collection of local monodromies.
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