Abstract :
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)).
