Сибирский математический журнал | |
Finite Groups with Given Weakly |
|
C. Cao1  | |
[1] University of Science and Technology of China | |
关键词: finite group; Ï-subnormal subgroup; Ï-permutable subgroup; weakly Ï-permutable subgroup; Ï-soluble group; supersoluble group; | |
DOI : 10.1134/S0037446618010172 | |
学科分类:数学(综合) | |
来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk | |
【 摘 要 】
Let G be a finite group and let Ï = {Ï i| i â I} be a partition of the set of all primes P. A set â of subgroups of G is said to be a complete Hall Ï-set of G if each nonidentity member of â is a Hall Ï i -subgroup of G and â has exactly one Hall Ï i -subgroup of G for every Ï iâ Ï(G). A subgroup H of G is said to be Ï-permutable in G if G possesses a complete Hall Ï-set â such that HA x= A x H for all A â â and all x â G. A subgroup H of G is said to be weakly Ï-permutable in G if there exists a Ï-subnormal subgroup T of G such that G = HT and H â© T ⤠H ÏG , where H ÏGis the subgroup of H generated by all those subgroups of H which are Ï-permutable in G. We study the structure of G under the condition that some given subgroups of G are weakly Ï-permutable in G. In particular, we give the conditions under which a normal subgroup of G is hypercyclically embedded. Some available results are generalized.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO201910252920590ZK.pdf | 187KB | download |