HEREDITARY UPPER RADICAL PROPERTIES AND DUAL SUPPLEMENTING RADICALS OF HEREDITARY RADICALS OF GROUPS

摘要

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.