On the socles of fully invariant subgroups of Abelian \(p\)-groups.
Reduced Abelian \(p\)-groups are considered. Socle-regular groups are introduced. A reduced Abelian \(p\)-group \(G\) is said to be socle-regular if for all fully invariant subgroups \(F\) of \(G\) there exists an ordinal \(\alpha\) (depending of \(F\)) such that \(F[p]=(p^\alpha G)[p]\). It is proved that every fully transitive group is socle-regular. Some basic properties of socle-regular groups are investigated. The classification of this class of groups is not made in the article.
scientific article; zbMATH DE number 5565246