有限群的弱ss-可补子群(英文)

On Weakly ss-Supplemented Subgroups of Finite Groups

有限群G的子群H叫做在G中弱ss-可补,如果存在G的子群K使得HK是G的次正规子群且H∩K≤HuG,其中HuG是G的含于H的最大次正规子群.该文利用Sylow子群的某些弱ss-可补子群来刻画有限群的可解性.

A subgroup H of a group G is said to be weakly ss-supplemented in G if there exists a subgroup K of G such that HK is a subnormal subgroup of G and H∩ K≤H,G, where HuG is the largest subnormal subgroup of G contained in H. In this paper, the solvability of a finite group G with rome subgroups of Sylow subgroups weakly ss-supple- mented in Gis characterized.