Locally Finite Suzuki–Higman 2-Groups

Abstract

We prove the following theorem. Let U be a locally finite Suzuki–Higman 2-group with respect to an automorphism group H. Then U and H are representable as the respective unions of ascending chains of finite subgroups U₁ < U₂ < . . . < U_n < . . . and H₁ < H₂ < . . . < H_n < . . ., in which case every subgroup U_n is a Suzuki 2-group with respect to H_n.