可解群的一些充分条件  

Some Sufficient Conditions of Soluble Groups

作　　者：何鸣[1] 江祥花[1] 

机构地区：[1]徐州师范大学数学系

出　　处：《徐州师范大学学报（自然科学版）》2003年第3期15-17,共3页Journal of Xuzhou Normal University(Natural Science Edition)

摘　　要：群G的一个子群H称为在G中弱c正规的,如果存在G的一个次正规子群K,使得G=HK且H∩K≤HG,其中HG=∩x∈GHx是包含在H中的G的最大正规子群.利用π Hall子群、奇阶Sylow子群和二极大子群的弱c正规性,给出了一个群为可解群的若干充分条件.A subgroup H of a group G is said to be weakly cnormal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG, where HG=CoreG∩x∈GHx is the largest normal subgroup of G that contained in H. In this paper, the authors give some sufficient conditions under which a group G is soluble one by using weakly cnormality of πHall subgroups, Sylow subgroup with odd order and second maximal subgroups of G.

关 键 词：可解群 充分条件 次正规子群 弱c正规子群 Π-HALL子群 奇阶Sylow子群 二极大子群 

分 类 号：O152.1[理学—数学]