Open Collections

Minimal degree of the automorphism group of primitive coherent configurations

Banff International Research Station for Mathematical Innovation and Discovery

The minimal degree of a permutation group $G$ is the minimum number of points not fixed by non-identity elements of $G$. Lower bounds on the minimal degree have strong structural consequences on $G$. In 2014 Babai proved that the automorphism group of a strongly regular graph with n vertices has minimal degree at least $cn$, with known exceptions. Strongly regular graphs correspond to primitive coherent configurations of rank 3. We extend Babai's result to primitive coherent configurations of rank 4. We also show that the result extends to non-geometric primitive distance-regular graphs of bounded diameter. The proofs combine structural and spectral methods. The results have consequences to primitive permutation groups that were previsouly known using the classification of finite simple groups (Cameron, Liebeck). The paper is available at arXiv:1802.06959.

Mathematics; Combinatorics; Group theory and generalizations; Discrete mathematics

video/mp4

Author affiliation: University of Chicago

2019-03-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68858

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/