Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Pure mathematics
Abstract
Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained.
DOI
https://doi.org/10.1016/j.jalgebra.2009.12.005
Recommended Citation
Goldsmith, B. & Danchev, P. On the socles of characteristic subgroups of Abelian p-groups. Journal of Algebra, vol. 323), pg. 3020-3028. doi:10.1016/j.jalgebra.2009.12.005
Publication Details
Journal of Algebra 323 (2010) 3020-3028 Available from the Publisher here www.elsevier.com/locate/jalgebra doi:10.1016/j.jalgebra.2009.12.005