Factorizations in finite groups

2011/05/10 by Vik. S. Kulikov, Kulikov, Vik. S. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR

paper · pdf · doi:10.48550/arxiv.1105.1939

29 pages

arxiv created 2011/05/10 · arxiv updated 2011/05/11

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 P¹ with given Galois group G and fixed collection of local monodromies.

Cited by

• A Note on Lagrange Subsets of Finite Groups

Related

• Factorization semigroups and irreducible components of Hurwitz space. II
• An answer regarding factorizations of finite groups
• Factorizations of finite groups
• Complete factorizations of finite groups
• Some problems about products of conjugacy classes in finite groups