The existence of complete mappings of SL(2,q), q≡3 modulo 4

In 1955, Hall and Paige conjectured that any finite group with a noncyclic Sylow 2-subgroup admits complete mappings. For the groups GL(2,q), SL(2,q), PSL(2,q), and PGL(2,q) this conjecture has been proved except for SL(2,q), q≡3 modulo 4. We prove the conjecture true for SL(2,q), q≡3 modulo 4.