若干中心商的阶为p6的有限p-群的不存在性问题

Nonexistence of Some Finite p-Groups of the Central Quotient Order of p6

基于Rodney James的文(The groups of order p6 (p an odd prime). Mathematics of Computation, 1980, 34 (150): 613-637. )和schreier扩张理论的思想,将被扩元作用于被扩群,通过换位子结构及幂结构得到存在与Z(G)为循环群的矛盾,进而得到一类中心商不存在的有限p-群,即给出当H为p6阶Φ39家族中的群且满足条件 时群G的不存在性问题。

Based on Rodney James’ paper (The groups of order p6 (p an odd prime), Mathematics of Compu-tation, 1980, 34 (150): 613-637. ) and the idea of schreier extension theory , act extended element on extended group, by the transposition substructure and the power structure we get the contradiction of Z(G) that is cyclical group, and then we get a class finite p-groups that the central quotient are nonexistence, that is to say when H are the groups of Φ39 family of order p6 and satisfied , we get the nonexistence of G.