摘要
利用子群的半正规性讨论了几类有限群的结构,得到如下主要结果:(l)极大子群超可解的有限群当其极大子群的极小子群半正规时,它不是超可解群就是如下三种群之一:(I)p~αq~β阶内-Abel群,p(?)q-1;(Ⅱ)p^(α+β)r(?)阶群,α≥2,β≥0,p~β=│φ(G)│,p^(α-1)||r—1,α^((?)~α+β)=c_1^(?)=c_2^(?)=…=c_(?)^(?)=1,c_ic_j=c_jc_i,i,j=1,2,…,p,c_(?)^(?)=c_(i+1),i=1,2,…,p-1,c_(?)^(?)=c_1^(?),t(mod r)指数p^(α-1);(Ⅲ)D_(2_q)型群;(2)极大子群可解的非Abel有限单群当其二次极大子群的极小子群半正规时,G恰为A_5.
A subgroup H of a finite group G is called to be semi-normal if theve exists a subgroup B such that G = HB and for any proper subgroup B, of B, HB1 is a proper subgroup of G. The following results were provrn with the concept :( 1 ) Let G be a finite group. If any maximal subgroup M of G is supersolvable and any minimal subgroups of M are semi-normal in M , then G is supersolvable, or is the following one of the three types :( I ) A inner- Abelian group of order( II ) A gruop of order( III ) A group of type of D2(2) A non-Abelian finite simple group G is a alternating group of degree 5 if any maximal subgroups of G are solvable and minimal subgroups of any 2-maximal subgroups M of G are semi-normal in M.
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1993年第3期265-268,共4页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
半正规
弱-半正规
有限群
极大子群
semi-normal
weak semi-normal
finite group
maximal subgroup
