On the Socles of Fully Inert Subgroups of Abelian p-Groups

Authors

Andrey R. Chekhlov, Tomsk State University
Peter V. Danchev, Bulgarian Academy of Sciences
Brendan Goldsmith, Technological University DublinFollow

Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

1.1 MATHEMATICS

Publication Details

Mediterranean Journal of Mathematics

Abstract

We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) and J. Algebra (2010).

Recommended Citation

Chekhlov, A., Danchev, P.V. & Goldsmith, B. (2020). On the socles of fully inert subgroups of abelian p-groups. Mediterranean Journal of Mathematics, ahead of print.