Entropy range problems and actions of locally normal groups

This paper deals with the problem of finding the range of entropy values resulting from actions of discrete amenable groups by automorphisms of compact abelian groups. When the acting group G is locally normal, we obtain an entropy formula and show that the full range of entropy values [0, ∞] occurs for actions of G. We consider related entropy range problems, give sufficient conditions for zero entropy and, as a consequence, verify the known relationship between completely positive entropy and mixing for these actions.