Isomorphisms Between Linear Groups Over Division Rings

Abstract

AbstractIn the present paper we completely describe the isomorphisms between projective elementary groups PSLn and PSLm (n ≥ 2, m ≥ 2) over division rings. It was found that such groups can be isomorphic only if n = m; the division rings are isomorphic or anti-isomorphic, except for the following groups:PSL(2,F7) and PSL(3,F2); PSL(2, F4) and PSL(2,F5).The idea is based on a deepening of the classical Hua's approach. This problem has been solved independently by H. Ren, Z. Wan and X. Wu using a different way