On infra-endomorphisms of infra-simple groups (Q1281303)

For a group \((G,+)\), written additively, an infra-subset \(I\) of \(G\) is a non-empty subset of \(G\) such that \(x\in I\) forces \(x+x\in I\). A group is infra-simple if the subset of all non-zero elements is an infra-subset with no proper infra-subsets. The authors show that an infra-simple group is precisely one which has only three infra-subsets. Such a group must be finite and of odd prime order. Finally, the near-ring generated by the infra-endomorphisms is the endomorphism ring.