p-进位域上可定义群的一个注记  

A Note on Definable Groups in the P-adic Field

作　　者：韩筱 陈国龙[2] HAN Xiao;CHEN Guolong(School of Mathematics Science,Huaibei Normal University,Huaibei 235000,China;Suzhou University,Suzhou 234000,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000 [2]宿州学院,安徽宿州234000

出　　处：《宿州学院学报》2020年第2期67-69,共3页Journal of Suzhou University

基　　金：安徽省高校自然科学研究重大项目(KJ2014ZD31)。

摘　　要：利用p-进位域(Qp,+,×,0,1)的模型论方法,研究了域Qp上的可定义群G,当G是局部可交换的,等价于瓖p连通代数群H(Qp),则可定义群G局部同构于H(Qp)且是可交换的,从而得到G是有限可交换的。证明了当G维数为1时,H为代数几何维数为1的连通代数群,p-进位域中一维可定义群是有限可交换的。Using the model theory method of the p-adic field(Qp,+,×,0,1),the definable group in the field Qp is studied.We prove that when G is locally commutative and is equivalent to the connected algebraic group over H Qp,then G is definably locally isomorphic to H(Qp),and commutative.Thu G is commutative-by-finite.When G is one-dimensional and H is a connected algebraic group of algebraic-geometric dimension 1,one-dimensional groups definable in the p-adics are commutative-by-finite.

关 键 词：p-进位域 可定义群 连通代数群 

分 类 号：O156.22[理学—数学]