Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks.
type: Item
instance of: scholarly article
title: Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks.
zbMATH Open document ID: 1068.20052
DOI: 10.1016/S0021-8693(03)00515-5
author: Martin W. Liebeck
author: Aner Shalev
published in: Journal of Algebra
publication date: 2004-11-19T00:00:00Z
review text: In this long and detailed paper, the authors consider Fuchsian groups occurring in many branches of mathematics as they mention. They use character-theoretic and probabilistic methods to study the space of homomorphisms from Fuchsian groups to symmetric groups. They obtain several applications such as counting the branched coverings of Riemann surfaces, subgroup growth and random finite quotients of Fuchsian groups, and random walks on symmetric groups. By showing that nearly all homomorphisms from a Fuchsian group to alternating groups are onto, they prove Higman's conjecture. They also establish a conjecture similar for symmetric groups to Higman's conjecture.
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20P05
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 2116873
zbMATH Keywords: Fuchsian groups
zbMATH Keywords: Riemann surfaces
zbMATH Keywords: coverings
zbMATH Keywords: symmetric groups
zbMATH Keywords: alternating groups
zbMATH Keywords: homomorphisms
zbMATH Keywords: subgroup growth
zbMATH Keywords: random finite quotients
zbMATH Keywords: random walks
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00515-5
OpenAlex ID: W2007263799
description: scientific article; zbMATH DE number 2116873