Augmentation quotients for Burnside rings of generalized dihedral groups

Chang, Shan. "Augmentation quotients for Burnside rings of generalized dihedral groups." Czechoslovak Mathematical Journal 66.4 (2016): 1165-1175. <http://eudml.org/doc/287538>.

@article{Chang2016,
abstract = {Let $H$ be a finite abelian group of odd order, $\mathcal \{D\}$ be its generalized dihedral group, i.e., the semidirect product of $C_2$ acting on $H$ by inverting elements, where $C_2$ is the cyclic group of order two. Let $\Omega (\mathcal \{D\})$ be the Burnside ring of $\mathcal \{D\}$, $\Delta (\mathcal \{D\})$ be the augmentation ideal of $\Omega (\mathcal \{D\})$. Denote by $\Delta ^n(\mathcal \{D\})$ and $Q_n(\mathcal \{D\})$ the $n$th power of $\Delta (\mathcal \{D\})$ and the $n$th consecutive quotient group $\Delta ^n(\mathcal \{D\})/\Delta ^\{n+1\}(\mathcal \{D\})$, respectively. This paper provides an explicit $\mathbb \{Z\}$-basis for $\Delta ^n(\mathcal \{D\})$ and determines the isomorphism class of $Q_n(\mathcal \{D\})$ for each positive integer $n$.},
author = {Chang, Shan},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized dihedral group; Burnside ring; augmentation ideal; augmentation quotient; generalized dihedral group; Burnside ring; augmentation ideal; augmentation quotient},
language = {eng},
number = {4},
pages = {1165-1175},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Augmentation quotients for Burnside rings of generalized dihedral groups},
url = {http://eudml.org/doc/287538},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Chang, Shan
TI - Augmentation quotients for Burnside rings of generalized dihedral groups
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 4
SP - 1165
EP - 1175
AB - Let $H$ be a finite abelian group of odd order, $\mathcal {D}$ be its generalized dihedral group, i.e., the semidirect product of $C_2$ acting on $H$ by inverting elements, where $C_2$ is the cyclic group of order two. Let $\Omega (\mathcal {D})$ be the Burnside ring of $\mathcal {D}$, $\Delta (\mathcal {D})$ be the augmentation ideal of $\Omega (\mathcal {D})$. Denote by $\Delta ^n(\mathcal {D})$ and $Q_n(\mathcal {D})$ the $n$th power of $\Delta (\mathcal {D})$ and the $n$th consecutive quotient group $\Delta ^n(\mathcal {D})/\Delta ^{n+1}(\mathcal {D})$, respectively. This paper provides an explicit $\mathbb {Z}$-basis for $\Delta ^n(\mathcal {D})$ and determines the isomorphism class of $Q_n(\mathcal {D})$ for each positive integer $n$.
LA - eng
KW - generalized dihedral group; Burnside ring; augmentation ideal; augmentation quotient; generalized dihedral group; Burnside ring; augmentation ideal; augmentation quotient
UR - http://eudml.org/doc/287538
ER -