Abstract
One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
The first author owes a great depth of gratitude to Dr. L. G. Peng for his many discussions and exchange of ideas and support.
Notes
Communicated by J. Zhang.