The structure of groups connected with automorphisms of cubic surfaces

In the paper we find the structure of groups given by systems of generators and power relations of a special kind, and we prove that the word problem and the conjugacy problem are solvable. The groups of birational automorphisms of minimal cubic surfaces belong to this class, and this enables us to solve a problem of Manin on the enumeration of automorphisms of finite order.
Bibliography: 4 titles.