有限群G的子群H称为G的弱P置换子群,如果存在G的次正规子群T使得G=HT且HnT≤H,其中Hc是由包含在H中的G的所有s-置换子群生成的群.设P是G的满足d是其最小生成元个数的一个P-子群.考虑P的d个极大子群构成的集合洲。(P)-{P1,P2,…,P4}且使得它们的交是P的Frattini子群Ф(P).该文主要研究了矾a(P)中的极大子群在G中满足弱r置换假设条件下G的结构,并推广了一些已知的结论.
Let G be a finite group. A subgroup H of G is said a weakly .s-Iermutahle subgroup of ; if there is a subaormal subgroup T of such that (i= HT anti llf'i I t1, where H; denotes the subgroup of H t4enerated hy II s-pt'rmutable subgroups of C; contained in H. I.el p be a prime number dividing / G /and P a Sylow p-suhgroup of G with the smallest generator numhcr d. There is a subset (P) = { Pl , P: , P,t ) of maximal sub-- groups of P such that [ P, =O(P), where,(P) denotes the Frattini subgroup of P. This pa per researches into the structure of G. under the assumption that every member in is ,t weakly s-permutable subgroup of G. The results unify and generalize some known ones.