n-Hopfian and n-co-Hopfian Groups

Abstract

For any natural number n we define and study the two notions of n-Hopfian and n-co-Hopfian abelian groups. These groups form proper subclasses of the classes of Hopfian and co-Hopfian groups, respectively, and some of their exotic properties are established as well. We also consider and investigate ω-Hopfian and ω-co-Hopfian modules over the formal matrix ring. 2010 Mathematics Subject Classification. 20K10; 20K20; 20K21. Key words and phrases. n-Hopfian groups, Hopfian groups, n-co-Hopfian groups, co-Hopfian groups.