COMMUTING AUTOMORPHISMS OF THE GROUP CONSISTING OF THE UNIT UPPER TRIANGULAR MATRICES

Let G be a group, an automorphism phi : G -> G is called a commuting automorphism, if for all x is an element of G, phi(x)x = x phi(x). Let U-n (F) be the group consisting of all n x n unit upper triangular matrices over a field F with characteristic char(F) not equal 2. In this paper, we prove that if n >= 4, a map phi : U-n (F) -> U-n (F) is a commuting automorphism of U-n (F) if and only if it is a central automorphism of U-n(F). Moreover, the set of the commuting automorphisms of U-n(F) is a normal subgroup of the automorphism group Aut(U-n(F)).