On the parametrization of subgroups of free groups. (Zur Parametrisierung von Untergruppen freier Gruppen.) (German) Zbl 0622.20017
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 M. Hall’s formula for the number of such subgroups [see Can. J. Math. 1, 187-190 (1949; Zbl 0031.34001)].
Reviewer: Ya.A.Bakhturin
MSC:
20E05 | Free nonabelian groups |
20E07 | Subgroup theorems; subgroup growth |
20B35 | Subgroups of symmetric groups |