Josef Dvořák, Jan Žemlička
Self-small products of abelian groups

Comment.Math.Univ.Carolin. 63,2 (2022) 145-157.

Abstract: Let A and B be two abelian groups. The group A is called B-small if the covariant functor {\rm Hom}(A,-) commutes with all direct sums B^{(\kappa)} and A is self-small provided it is A-small. The paper characterizes self-small products applying developed closure properties of the classes of relatively small groups. As a consequence, self-small products of finitely generated abelian groups are described.

Keywords: self-small abelian group; slender group

DOI: DOI 10.14712/1213-7243.2022.020
AMS Subject Classification: 20K40 20K20 20K21