【摘要】 设G为有限群,称G的子群H在G中S-拟正规,如果H和G的每个Sylow子群相乘可换.利用子群的S-拟正规性给出了有限群成为幂零群或超可解群的一些充分条件,并得到了有限群G的2-极大子群在G中S-拟正规时G的一个完全分类定理.更多还原

【Abstract】 Let G be a finite group.A subgroup H of a group G is said to be S-quasinormal in G if H permutes with every Sylow subgroup of G.In this paper,in terms of S-quasinormal subgroups,some sufficient conditions for a finite group to be supersolvable or nilpotent are obtained.Under the condition that 2-maximal subgroup of G is S-quasinormal in G,a complete classification of G is obtained.更多还原