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Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups |
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| Authors: | Xuemei Li Zhirang Zhang |
| Affiliation: | 1. School of Mathematics , Sichuan University , Chengdu , Sichuan , China;2. College of Applied Mathematics , Chengdu University of Information Technology , Chengdu , Sichuan , China lxm198022@126.com;4. College of Applied Mathematics , Chengdu University of Information Technology , Chengdu , Sichuan , China |
| 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. |
| Keywords: | Hereditary radical properties of groups Hereditary upper radical properties of groups Strongly semisimple groups The dual pair of supplementing radical properties The supplementing radical property |