Automorphisms Of The Maximal Unipotent Subgroups Of Ree Group And Suzuki Group

Let 2^F₄(F), 2^B₂(F) be the Ree group of type F₄ and the Suzuki group over a finite field F of characteristic 2, respectively. Let 2^G₂(F) be the Ree group of type G₂ over a finite field of characteristic 3. These groups are also called twisted chevalley groups. They are generated by the unipotent subgroups, U¹ and V¹. This paper aims to determine the automorphism group of the maximal umpotent subgroup U¹. The main theorem is as follow:Let U¹ be the maximal unipotent subgroup of Ree group, then any automorphism φ of U¹ can be expressed as a product of diagonal, field, inner and central automorphisms, i.e., φ = d_x · η_f · σ_a · μ_c, where d_x, η_f, σ_a and μ_c are diagonal, field, inner and central automorphisms, respectively, of U¹.For the case of 2^B₂(F), we also determine the automorphism group of U¹. The result is: any automorphism φ of U¹ can be expressed as a product of diagonal, field, and central automorphisms, i.e.,φ = d_x ·f· μ_c, where d_x, f, and μ_c are diagonal, field, and central automorphisms, respectively, of U¹.