Dominions in decomposable varieties

Dominions, in the sense of Isbell, are investigated in the context of decomposable varieties of groups. An upper and lower bound for dominions in such a variety is given in terms of the two varietal factors, and the internal structure of the group being analyzed. Finally, the following result is established: If a variety has instances of nontrivial dominions, then for any proper subvariety of , also has instances of nontrivial dominions. Received September 2, 1998; accepted in final form October 24, 1999.