  Translation association schemes are constructed from actions of finite groups
on finite abelian groups satisfying certain natural conditions. It is also
shown that the mere existence of maps from finite groups to themselves sending
each element in their groups to its `adjoint' entails the self-duality of the
constructed association schemes. Many examples of these, including Hamming
scheme and sesquilinear forms schemes, are provided. This con- struction is
further generalized to show the duality of the association schemes coming from
actions of two finite groups on the same finite abelian group. An example of
this is supplied with weak Hamming schemes.
