Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Abstract
The classification of the fully invariant subgroups of a reduced Abelian p-group is a difficult long-standing problem when one moves outside of the class of fully transitive groups. In this work we restrict attention to the socles of fully invariant subgroups and introduce a new class of groups which we term socle-regular groups; this class is shown to be large and strictly contains the class of fully transitive groups. The basic properties of such groups are investigated but it is shown that the classification of even this simplified class of groups, seems extremely difficult.
Recommended Citation
Goldsmith, Brendan and Danchev, P. V., "On the socles of fully invariant Abelian p-groups" (2009). Articles. 38.
https://arrow.tudublin.ie/scschmatart/38