Augmentation quotients for Burnside rings of some finite $p$-groups

Proceedings of the Indian Academy of Sciences. Mathematical sciences

SHAN CHANG^1¹ 

[1] School of Mathematics, Hefei University of Technology, Hefei 230009, China^1

关键词: Finite $p$-group;    Burnside ring;    augmentation ideal;    augmentation quotient;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $G$ be a finite group, $\Omega(G)$ be its Burnside ring and $\Delta(G)$ the augmentation ideal of $\Omega(G)$. Denote by $\Delta^{n}(G)$ and $\mathcal{Q}_{n}(G)$ the $n$-th power of $\Delta(G)$ and the $n$-th consecutive quotient group $\Delta^{n}(G)/\Delta^{n+1}(G)$, respectively. This paper provides an explicit $\mathbb{Z}$-basis for $\Delta^{n}(\mathcal{H})$ and determine the isomorphism class of $\mathcal{Q}_{n}(\mathcal{H})$ for each positive integer $n$, where $\mathcal{H} = \langle g, h| g^{p^{m}} = h^{p} = 1, h^{−1}gh = g^{p^{m−1}+1}\rangle$, $p$ is an odd prime

【 授权许可】

CC BY