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2002•Journalof Southwest China Normal UniversityRequires access

On Inner-Finite Infinite Simple Groups

Yu Da

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Abstract

By investigating the innerfinite infinite simple groups, the authors have proved: if a nonabelian innerfinite group has an involution, then it is not a simple group; And also the innerfinite infinite simple groups are all innersovluble. Depending on these results, the authors have obtained some sufficient and necessary conditions for a group to be innernilpotent, innerabelian, or innercyclic respectively when this group is an innerfinite infinite simple group.

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What this paper is about

By investigating the innerfinite infinite simple groups, the authors have proved: if a nonabelian innerfinite group has an involution, then it is not a simple group; And also the innerfinite infinite simple groups are all innersovluble. Depending on these results, the authors have obtained some sufficient and necessary conditions for a group to be innernilpotent, innerabelian, or innercyclic respectively when this group is an innerfinite infinite simple group.

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Available abstract

By investigating the innerfinite infinite simple groups, the authors have proved: if a nonabelian innerfinite group has an involution, then it is not a simple group; And also the innerfinite infinite simple groups are all innersovluble. Depending on these results, the authors have obtained some sufficient and necessary conditions for a group to be innernilpotent, innerabelian, or innercyclic respectively when this group is an innerfinite infinite simple group.

Key concepts: Simple group, Mathematics, Simple (philosophy), Involution (esoterism), Classification of finite simple groups, Group (periodic table), Abelian group, Nilpotent

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