Geodesic
Most rigid representation and Cayley index of finitely generated groups
Paul-Henry Leemann1 ; Mikael de la Salle2
1Université de Neuchâtel
2CNRS, UMPA ENS de Lyon
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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If $G$ is a group and $S$ a generating set, $G$ canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the Cayley index of the group. In a recent series of works, we have characterized the infinite finitely generated groups with Cayley index $1$. We complement this characterization by showing that the Cayley index is $2$ in the remaining cases and is attained for a finite generating set.
DOI : 10.37236/10512
Classification : 05E18, 20B25, 05C25, 05C63, 20F05, 20F65

Paul-Henry Leemann  1   ; Mikael de la Salle  2

1 Université de Neuchâtel
2 CNRS, UMPA ENS de Lyon 
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     title = {Most rigid representation and {Cayley} index of finitely generated groups},
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Paul-Henry Leemann; Mikael de la Salle. Most rigid representation and Cayley index of finitely generated groups. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10512

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