Estimation of the structure of K2(4C2r)

DENG Wenchao; TANG Guoping

doi:10.7523/j.ucas.2021.0043

Journal of University of Chinese Academy of Sciences >

2023 , Vol. 40 >Issue 4: 453 - 455

DOI: https://doi.org/10.7523/j.ucas.2021.0043

Research Articles

Estimation of the structure of K₂(₄C_2^r)

DENG Wenchao ,
TANG Guoping

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School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2021-04-27

Revised date: 2021-05-12

Online published: 2021-05-12

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Abstract

We already know K₂(

₄C₂)=(C₂)²,K₂(

₄C₄)=(C₂)³ from a paper of Zhang Yakun and Tang Guoping(K₂ for a kind of special finite group rings). In this paper, we got a set of simplified generators of K₂(

₄C_2^r) by calculating Dennis-Stein symbol in relative K₂ group. Then we got the basis for K₂(

₄C₂) and K₂(

₄C₄), and we got to know K₂(

₄C₈)=(C₂)^k, 3 ≤ k ≤ 5, K₂(

₄C_2^r)=(C₂)^l,l ≤ 2^r-1+1。

Key words： K₂ group; group ring; Dennis-Stein symbol

Cite this article

DENG Wenchao , TANG Guoping . Estimation of the structure of K₂(₄C_2^r)[J]. Journal of University of Chinese Academy of Sciences, 2023 , 40(4) : 453 -455 . DOI: 10.7523/j.ucas.2021.0043

References

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[2] Hatcher A. Pseudo-iostopy and K₂[C]//Bass H. "Classical" Algebraic K-Theory, and Connections with Arithmetic. Berlin:Springer, 1973:328-336.
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[5] 张亚坤, 唐国平. 一类特殊有限群环的K₂-群[J]. 中国科学院大学学报, 2018, 35(6):721-723.DOI:10.7523/j.issn.2095-6134.2018.06.001.

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