R-Hopfian and L-co-Hopfian Abelian Groups (with an Appendix by A.L.S. Corner on Near Automorphisms of an Abelian Group)

Abstract

The notions of Hopfian and co-Hopfian groups are well known in both non-commutative and Abelian group theory. In this work we begin a systematic investigation of natural generalizations of these concepts and, in the case of Abelian p-groups, give a complete characterization of the generalizations in terms of the original concepts. The final section of the paper contains an unpublished result of A.L.S. Corner on near automorphisms which has been useful in a number of contexts.