On automorphisms of a distance-regular graph with intersection array 44, 30, 5; 1, 3, 40

Abstract

Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array 44, 30, 5; 1, 3, 40. Let G = Aut(Γ) is nonsolvable group. If Γ is arc-transitive then G is is an extension of some group P by PGL2(11), |P: O3(P)| = 2, |Ga: Pa| = 11 and |P: Pa| = 9. © 2019, Sobolev Institute of Mathematics.