On the parametrization of subgroups of free groups.
type: Item
instance of: scholarly article
title: On the parametrization of subgroups of free groups.
zbMATH Open document ID: 0622.20017
author: Andreas W. M. Dress
author: Reinhard Franz
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138363
review text: Using Cayley diagrams the authors establish a bijective correspondence between the set of subgroups of index \(n\) in a free group with \(k\) generators and a set of permutations in \(n+1\) symbols satisfying certain conditions. This leads to a new proof of \textit{M. Hall}'s formula for the number of such subgroups [see Can. J. Math. 1, 187-190 (1949; Zbl 0031.34001)].
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20B35
zbMATH DE Number: 4008648
zbMATH Keywords: numbers of subgroups
zbMATH Keywords: Cayley diagrams
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: free groups
zbMATH Keywords: sets of permutations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4008648