由 Ω 子群所决定的格序群的结构  

The Structure of Lattice Ordered Groups Determined by the Ω-Subgroups

作　　者：郑熙强[1] 

机构地区：[1]南昌航空工业学院

出　　处：《南昌航空工业学院学报》1997年第1期27-32,共6页Journal of Nanchang Institute of Aeronautical Technology（Natural Science Edition）

基　　金：江西省自然科学基金

摘　　要：设Ｇ是一个格序群，Π（Ｇ）、Πｍ（Ｇ）、Ｐ（Ｇ）、Ｃ（Ｇ）分别是Ｇ的素子群、极小素子群、极子群、凸ｌ－子群集合，Ω（Ｇ）是Ｐ（Ｇ）在Ｃ（Ｇ）中生成的闭子格。Ω（Ｇ）的元素称为Ｇ的Ω－子群。本文利用Ω－子群来研究格序群的结构，得到了一系列新的、重要的Ｌ－群特性，对投射Ｌ－群给出了一个重要的新刻画，而且在投射Ｌ－群情形解决了Ｐ·Ｃｏｎｒａｄ提出的问题“ＷｈｅｎｉｓＣ（Ｇ）＝Ｐ？”Let G be an l group,П m(G)the set of its prime subgroups,П m(G)the set of its minimal prime subgroups ,P(G)the set of its polar subgroups ,C(G)the lattice of its convex l subgroups and Ω(G)the complete sublattice of C(G)generated by P(G).The elements of Ω(G)aredefined as the Ω subgroups of G.In this paper, the structure of lattice ordered groups was investigated with the help of their Ω subgroups .Some important new features of Lgroups were obtained and an important new description on the projectable l groups were given.Under the assumption that G is projectable we got the answer to the question:'when is C(G)=P?',which was proposed by P·Conrad.

关 键 词：格序群 极子群 根类 Ω子群 

分 类 号：O153.1[理学—数学]