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Original Articles

Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups

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Pages 3282-3293 | Received 28 Mar 2012, Published online: 04 Jun 2015
 

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.

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