On the parametrization of subgroups of free groups. (Q1090762)
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scientific article; zbMATH DE number 4008648
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the parametrization of subgroups of free groups. |
scientific article; zbMATH DE number 4008648 |
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On the parametrization of subgroups of free groups. (English)
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1987
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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)].
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numbers of subgroups
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Cayley diagrams
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subgroups of finite index
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free groups
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sets of permutations
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