On algebraic normalisers of maximal tori in simple groups of Lie type

Abstract

Let 𝐺 be a finite simple group of Lie type and let 𝑇 be a maximal torus of 𝐺. It is well known that if the defining field of 𝐺 is large enough, then the normaliser of 𝑇 in 𝐺 is equal to the algebraic normaliser N ⁢ ( G , T ) N(G,T) . We identify explicitly all the cases when N G ⁢ ( T ) N_{G}(T) is not equal to N ⁢ ( G , T ) N(G,T) .