2012•Journal of Beijing Union UniversityRequires access

The Influence of Sylow Subgroups and Its Maximal Subgroups on the Finite Groups

Zhang Li-ying

Abstract

By using the completely conditional permutability of the Sylow subgroups and its maximal subgroups of finite group G,the sufficient conditions for a finite group G to be supersolvable are proved and the results are generalized to formations.Moreover,the sufficient condition for a saturated formation containing the class of all finite supersolvable groups is also obtained,and some known results are generalized.

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Key concepts: Sylow theorems, Mathematics, Locally finite group, Class (philosophy), Finite group, Pure mathematics, Group (periodic table), Combinatorics