有限群的δ-置换子群

Onδ-Permutable Subgroups of Finite Groups

假定δ是有限群G的Sylow子群的完全集,即对每个|G|的素因子p,集合δ仅包含G的一个Sylow p-子群.若群G的子群H置换δ中的所有元素,则称子群H在G中δ-置换.利用准素数子群的δ-置换性研究了有限群的结构,得到了超可解群的若干新的判别准则.

Letδbe a complete set of Sylow subgroups of a finite group G.Then,δcontains exactly one Sylow p-subgroup of G for each prime p dividing the order of G.A subgroup H of G is said to beδ-permutable if H permutes with each member ofδ.The structures of finite groups withδ-permutability of primary subgroups are investigated and some new determination criteria of supersolvable groups are obtained.