Self-small $\mathrm{SP}$-groups with clean endomorphism rings

In this work, some aspects of cleanness of endomorphism rings of $\mathrm{SP}$-groups are considered. These groups form one of the classes of mixed Abelian groups. The cleanness of endomorphism rings of self-small $\mathrm{SP}$-groups is proved. Some sufficient conditions are found for the converse proposition to hold.