JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 37 - 47
(April 2005)
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THE SEMIPERMUTABLE SUBGROUP AND FINITE NILPOTENT GROUP
Minbang Su (P. R. China)
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Abstract: Let Z be a complete set of Sylow subgroups of a finite group G, that is, Z contains exactly one and only one Sylow p-subgroup of G for each prime pμ/span>p(G). A subgroup H of G is said to be Z -semipermutable in G if H permutes with every member of Z whose order is prime to | H |. We give a characteristic condition of finite nilpotent group under the assumption that some minimal subgroups of G are Z-semipermutable in G. Our results improve and extend some recent results. |
Keywords and phrases: p -semipermutable subgroup, Z-semipermutable subgroup, nilpotent group, p-nilpotent group, saturated formation. |
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