## 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

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