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 .%目的 确定当 H为p6阶Φ37,Φ42,Φ43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 p6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)| = p6的LA-猜想的反例.
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