对K_(2)(Z_(4)C_(2^(r)))结构的估计  

Estimation of the structure of K_(2)(Z_(4)C_(2^(r)))

作　　者：邓文超 唐国平 DENG Wenchao;TANG Guoping(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2023年第4期453-455,共3页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11771422)资助。

摘　　要：由张亚坤和唐国平2018年的论文(张亚坤,唐国平.一类特殊有限群环的K_(2)-群,中国科学院大学学报)得K_(2)(Z_(4)C_(2))=(C_(2))^(2),K_(2)(Z_(4)C_(4))=(C_(2))^(3)。借助相对K_(2)群,通过计算Dennis-Stein符号给出K_(2)(Z_(4)C_(2~r))的一组简化的生成元,在此基础上给出K_(2)(Z_(4)C_(2))和K_(2)(Z_(4)C_(4))的基底,并得到K_(2)(Z_(4)C_(8))=(C_(2))^(k),3≤k≤5,K_(2)(Z_(4)C_(2^(r)))=(C_(2))^(l),l≤2^(r-1)+1。We already know K_(2)(_(4)C_(2))=(C_(2))^(2),K_(2)(_(4)C_(4))=(C_(2))^(3) from a paper of Zhang Yakun and Tang Guoping(K_(2) for a kind of special finite group rings).In this paper,we got a set of simplified generators of K_(2)(_(4)C_(2)r)by calculating Dennis-Stein symbol in relative K_(2) group.Then we got the basis for K_(2)(_(4)C_(2))and K_(2)(_(4)C_(4)),and we got to know K_(2)(Z_(4)C_(8))=(C_(2))^(k),3≤k≤5,K_(2)(Z_(4)C_(2^(r)))=(C_(2))^(l),l≤2^(r-1)+1。

关 键 词：K_(2)群 群环 Dennis-Stein符号 

分 类 号：O154.3[理学—数学]