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Mat. Sb., 2013, Volume 204, Number 2, Pages 87–116 (Mi msb7919)  

This article is cited in 3 scientific papers (total in 3 papers)

Factorizations in finite groups

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.
Bibliography: 9 titles.

Keywords: factorization semigroups, irreducible components of the Hurwitz space of coverings of the projective line.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00185
Ministry of Education and Science of the Russian Federation НШ-4713.2010.1
11.G34.31.0023


DOI: https://doi.org/10.4213/sm7919

Full text: PDF file (676 kB)
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English version:
Sbornik: Mathematics, 2013, 204:2, 237–263

Bibliographic databases:

Document Type: Article
UDC: 512.53+512.544+512.772.5
MSC: Primary 20F05, 20F10, 20M99; Secondary 20F06
Received: 04.08.2011 and 30.10.2012

Citation: Vik. S. Kulikov, “Factorizations in finite groups”, Mat. Sb., 204:2 (2013), 87–116; Sb. Math., 204:2 (2013), 237–263

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. Math., 77:3 (2013), 594–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. F. A. Bogomolov, V. S. Kulikov, “The ambiguity index of an equipped finite group”, Eur. J. Math., 1:2 (2015), 260–278  mathnet  crossref  mathscinet  zmath  scopus
    3. V. I. Zvonilov, S. Yu. Orevkov, “Compactification of the Space of Branched Coverings of the Two-Dimensional Sphere”, Proc. Steklov Inst. Math., 298 (2017), 118–128  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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