几类中心商同构于p6阶群的LA-猜想的反例

目的:确定当H为p^6阶Φ_{37}，Φ_{42}，Φ_{43}家族中的群且满足条件G/Z(G)≌H时群G是不存在的。方法:通过P.Hall 恒等式、 换位子结构、亚交换群的幂结构等方法。结果与结论:证明了几类中心循环且中心商的阶为p^6的有限p-群G是不存在的，即这样的群G是满足条件|G/Z(G)|=p^6的LA-猜想的反例。

Counterexamples of LA-conjecture of some classes of groups in which central quotients are isomorphic to the group of order p6

Purposes—To determine that the Group G is nonexistent when H is the groups of the families of Φ37,Φ42and Φ43w hich belong to order p6and meets G/Z(G)(≈) H .Methods—T he methods of P .Hall identical equation ,commutator structure ,metabelian group for power structure and the like are adopted to accomplish the said purpose .Result and Conclusion—Some finite p-groups of w hich Z(G) are cyclical and the orders of their central quotients are p6prove nonexistent ,that is to say ,the groups like these that meet |G/Z(G)|= p6are the counterexample of LA-conjecture .