Unique maximal rings of functions

摘要

For several classes of groups G, we characterize when the near-ring M-0(G) of 0-preserving selfmaps on G contains a unique maximal ring. Definitive results are obtained for finite Abelian, finite nilpotent, and finite permutation groups. As an application, we determine those finite groups G such that all rings in M-0(G) are commutative.