摘要
主要用有限单群理论及其素图知识讨论了极大幂零子群的阶为素数幂的有限群,给出这类群结构的一些刻化。设G有限群,G的极大幂零子群的阶都是素数幂,则G为下列之一:1)G为p 群;2)G为pαqβ阶群,此时G为Frobenius群或2 Frobenius群;3)存在H G,H为2 群,G/H同构下列群之一:A5、A6、A6·23、L2(7)、L2(8)、L2(17)、L3(4)、2B2(8)、2B2(32)。进一步可得:当G/H≌L2(7)时,有G≌L2(7),其中H是2 群;当G/H≌L3(4)时,有G≌L3(4),其中H是2 群。
In this article we discuss the finite group that the orders of maximal nilpotence subgroups are prome power and obtain classes of the finite group.The main result is :Let G be finite group and the orders of maximal nilpotence subgroups of G are prome power,Then G is one of the following groups:1) p-group contains G;2) Frobenius gronp or 2-Frobenius group and the order of G is p~αq~β.3) There is an normal subgroup H of G,H is 2-group,G/H is isomorphic to one of the following groups;A_5、A_6、A_6·2_3、L_2(7)、L_2(8)、L_2(17)、L_3(4)、~2B_2(8)、~2B_2(32).Moreover,When G/H is isomorphic to L_2(7),G is isomorphic to L_2(7).Where H is 2-group;When G/H is isomorphic to L_3(4),G is isomorphic to L_3(4),where H is 2-group.
出处
《重庆师范大学学报（自然科学版）》
CAS
2004年第1期17-19,共3页
Journal of Chongqing Normal University:Natural Science
关键词
极大幂零子群
素数幂
有限群
素图
K3-单群
外自同构群
有限单群
finite group
maximal nilpotent subgroup
prime graph
K_3-simple group
outer automorphism group
finite simple group
