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关于CAP-嵌入子群的一个注记

A Note on CAP-embedded Subgroup
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摘要 假设G是一个有限群,H是G的一个子群。H称为G的CAP-子群,如果H覆盖或远离G的每个主因子;H称为G的CAP-嵌入子群,如果对于H的每个素因子p,存在G的某个CAP-子群K使得H的某个Sylow p-子群也是K的一个Sylow p-子群。利用一些素数幂阶子群的CAP-嵌入性研究有限群的p-幂零性,推广了前人的一些结果。 Suppose G is a finite group and H is a subgroup of G.H is said to be a CAP-subgroup of G if H covers or avoids every chief factor of G;H is said to be a CAP-embedded subgroup of G if,for each prime p dividing the order of H,there exists a CAP-subgroup K of G so that a Sylow p-subgroup of H is also a Sylow p-subgroup of K.We investigate the influence of CAP-embedded subgroups of prime power order on the p-nilpotency of finite groups.Some recent results are generalized.
作者 李长稳 於遒
出处 《四川理工学院学报(自然科学版)》 CAS 2010年第3期264-266,共3页 Journal of Sichuan University of Science & Engineering(Natural Science Edition)
基金 国家自然科学基金项目(10771180) 徐州师范大学科研基金资助项目(09XLB01)
关键词 CAP-嵌入子群 P-幂零 Sylowp-子群 CAP-embedded subgroup p-nilpotent Sylow p-subgroup
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