Self-small products of abelian groups

2021/02/23 by J. Dvořák, Jan Žemlička, Dvořák, Josef +1
Mathematics · #20K21) #20K40 (20K20 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2102.11443

openalex publication_date 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For abelian groups A, B, A is called B-small if the covariant functor Hom(A,-) commutes with all direct sums B^(κ) 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.

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