收稿日期: 2010-09-06
修回日期: 2010-09-26
网络出版日期: 2011-07-15
基金资助
Supported by National Natural Science Foundation of China(11071247)
Calculation of K2(F2[C4×C4])
Received date: 2010-09-06
Revised date: 2010-09-26
Online published: 2011-07-15
Supported by
Supported by National Natural Science Foundation of China(11071247)
把K2(F2[C4×C4])的计算归结为计算截断多项式环F2C4[t]/(t4)的相对K2－群K2(F2C4[t]/(t4),(t)). 运用Dennis-Stein符号及它们之间的关系进行细致的分析计算,给出了K2(F2[C4×C4])的一个极小生成元集并最终确定了K2(F2[C4×C4])=C34 ⊕ C92.
关键词： K2-群; Dennis-Stein符号; 群环
陈虹 , 高玉彬 , 唐国平 . K2(F2[C4×C4])的计算[J]. 中国科学院大学学报, 2011 , 28(4) : 419 -423 . DOI: 10.7523/j.issn.2095-6134.2011.4.001
First, we reduce the calculation of K2(F2[C4×C4]) to that of the relative K2-group K2(F2C4[t]/(t4),(t)) of the truncated polynomial ring F2C4[t]/(t4). Then we give a minimal generating set of K2(F2[C4×C4]) by subtle calculations of Dennis-Stein symbols. Finally we show that K2(F2[C4×C4])=C34 ⊕ C92.
Key words： K2-group; Dennis-Stein symbols; group ring
[1] Magurn B. Explicit K2 of some finite group rings
[J]. J Pure Appl Algebra, 2007, 209: 801-911.
[2] Gao Y B, Tang G P. K2 of finite abelian group algebras
[J]. J Pure Appl Algebra, 2009, 213:1201-1207.
[3] Stienstra J. On K2 and K3 of truncated polynomial rings //Algebraic K-theory (Evanston,1980), Lecture notes in Math 854. Berlin: Springer, 1971.
[4] Oliver R. Lower bounds for K2top (Zpπ) and K2(Zπ)
[J]. J Algebra, 1985, 94(2): 425-487.
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