Slender groups and related concepts

Abelian Groups in Russia

“…He expanded the concept of a slender group in the sense of Loš to the concept of a generalized slender mixed abelian group [134]. Rychkov also obtained several nice theorems characterizing homomophisms from direct products of groups to generalized slender groups and, dually, from dual slender groups to direct sums of groups [147]. Rychkov proved the following generalization of a well-known theorem of Loš by showing that a quotient group i G i / i G i is algebraically compact if and only if all but countably many factors are algebraically compact [135].…”