由二元生成子群确定的性质

ON PROPERTIES DETEMINED BY THE TWO-GENERATOR SUBGROUPS

我们记群类x∈TD,若x满足下面性质:“G∈x当且仅当G的每个二元生成子群G_1∈x”文中我们通过对极小反例的分析及扩张方式得到一个较一般的判定TD性质的方法。使一些已知群类的TD性质能非常简单地证明并通过扩张可知大多数常见的子群闭的群类都具有TD性质。

ON PROPERTIES DETEMINED BY THE TWO-GENERATOR SUBGROUPS We write x∈TD if x is of the property: 'G∈x if and only if G_1∈x for every two-generator subgroup G_1 of G' . In this paper, We have established a general method to determine x∈TD by examining the structure of minimal non-x-group. We have proved that if x∈TD, then N^kx∈TD.We easily find that x∈TD is true for many common classes of finite groups,