3-3群图的构造

The Constructions of 3-3 Group-graph

本文用局部分析的方法研究了下列问题:若群G由它的两个有限子群生成,G=<P_1,P_2>,其中P_1∩P_2在P_1、P_2的指数都为3,且P_1∩P_2不包含G的非平凡正规子群,则总共有15个群对(P_1,P_2) 满足以上条件。用这种方法,不但简化了证明过程,突出了问题的本质,还可以得出有限单群的新结论。

In this paper, the author studied the following problem with the method of group local analysis: If the group G is generated by two of its finite sub groups, G=(P_1, P_2)in which, the index of P_1∩P_2 in P_1 or P_2 is 3, and there is no non-trivial normal subgroups of G contained in P_1 P_2, then there are altogether 15 group pairs (P_1, P_2) satisfy the above conditions. This method not only can simplify the original proof, stress its intrinsic quality but also get the new conclusion for the finite simple group.