Outer Automorphisms of Upper Triangular Matrices Original Research Article

The outer automorphism group of the upper triangular matrices over the field of two elements is calculated. A. J. Weir (Proc. Amer. Math. Soc.6 (1955), 454-464) performed a similar calculation for Fields of odd characteristic, and we borrow the term extremal automorphism from his work. The results have implications in the study of stable splittings: the classifying space of Un has three dominant summands when n = 4 and only one dominant summand when n ≥ 5, in the sense of G. Nishida (Stable homotopy type of classifying spaces of finite groups, preprint (1986)).