格群的子积根式类（Ⅰ）

Subproduct Radical Classes of l Groups

一组ｌ－群Ｕ称作一个子积根式类，如果它封闭于取凸ｌ－子群、作凸ｌ－子群的并及作完全次直积．本文证明了ｌ－群的子积根式类由其对应的子积根式映射所唯一决定，并证明了两个子积根式类的积还是一个子积根式类．

A family R of l groups is considered as a subproduct radical class if R is clsoed under taking convex l subgroups, forming joins of convex l subgroups and forming direct products. In this paper it is proved that a subproduct radical class of l groups is uniquely determined by the corresponding subproduct radical mapping, and that the product of two subproduct radical classes is also a subproduct radical class. Finally, the structure for subproduct radical class generated by a family of l groups is given.