Rigid automorphisms of linking systems

Abstract A rigid automorphism of a linking system is an that restricts to the identity on Sylow subgroup. inner conjugation by element in center At odd primes, it known each centric inner. We prove group outer automorphisms at prime $2$ elementary abelian and splits over subgroup automorphisms. In second result, we show if finite G for , then $p'$ -order modulo automorphisms, provided has no nontrivial normal -subgroups. present two applications this last one tame fusion systems.