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Factorizations in finite groups. (English. Russian original) Zbl 1290.14020

Sb. Math. 204, No. 2, 237-263 (2013); translation from Mat. Sb. 204, No. 2, 87-116 (2013).
The paper under review is a sequel of the author’s previous work [Izv. Math. 75, No. 4, 711–748 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 4, 49–90 (2011; Zbl 1242.14026)]. There, he introduced a structure of semigroup on the set of irreducible components of the Hurwitz space of coverings of degree \(d\) of \(\mathbb{P}^1\) of fixed ramification type. The purpose of this was to study the geometry of Hurwitz spaces, by investigating representatives of conjugacy classes in the Galois group of the covering.
Now, the author gets a necessary condition for the uniqueness of factorization of elements of a group \(G\), when the factors belong to a union of some conjugacy classes in \(G\), which are defined by monodromy. The condition is also sufficient when the number of factors in each conjugacy class is big enough.

MSC:

14H30 Coverings of curves, fundamental group
20M99 Semigroups

Citations:

Zbl 1242.14026
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References:

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