The state and the mayor's office in San Francisco are conducting separate investigations into the deaths of at least five children who were under the supervision of that city's Social Services Department. The investigations were spurred by the recent death of a 14-month-old boy who allegedly was beaten by an Oakland man and his transvestite lover. The two men, who posed as man and wife, were adopting the child. Gregory Rogers, 29, and Alvin Woodard, 24, have been charged with murder, and the license of the Black Adoption Placement and Research Center of Oakland, the private agency handling the adoption, has been temporarily suspended. Mayor Dianne Feinstein said a special city commission will review all deaths in foster care during the past two years and all placement practices. The state's community care licensing agency is examining eight cases. About 1,400 children in San Francisco are in foster care.