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

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/129/01/0009

• Keywords

Finite $p$-group; Burnside ring; augmentation ideal; augmentation quotient

• Abstract

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

• Author Affiliations

1. School of Mathematics, Hefei University of Technology, Hefei 230009, China

• Proceedings – Mathematical Sciences

Volume 130, 2020
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