Near-rings of invariants. II

Abstract:

Let $E$ be the equivalence relation determined by the orbits of a group $G$ acting on a set $X$ and let $K$ be a group. Using a "sandwich" function $\varphi :X/E \to K,\;M(X,G,K,\varphi ) = \{ f:X \to K|f\;{\text {is constant on each}}\;E{\text {-class}}\}$ is a near-ring, the near-ring of invariants determined by $(X,G,K,\varphi )$. In this paper we continue the study of the transfer of information between the structure of the near-ring of invariants and properties of the group action $(G,X)$, the group $K$, and the function $\varphi :K \to X/E$.