Finite Groups with S-permutable n-maximal Subgroups |
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Authors: | Guohua Qian |
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Institution: | 1. Department of Mathematics , Changshu Institute of Technology , Changshu , Jiangsu , P.R. China ghqian2000@sohu.com |
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Abstract: | Let G be a finite group and M n (G) be the set of n-maximal subgroups of G, where n is an arbitrary given positive integer. Suppose that M n (G) contains a nonidentity member and all members in M n (G) are S-permutable in G. Then any of of the following conditions guarantees the supersolvability of G: (1) M n (G) contains a nonidentity member whose order is not a prime; (2) all nonidentity members in M n (G) are of prime order, and all cyclic members in M n?1(G) of order 4 are S-permutable in G. |
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Keywords: | Finite group n-Maximal subgroup S-Permutable subgroup Supersolvable group |
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