论文标题
对称组的积分双燃烧环$ \ text {s} _3 $
The integral double Burnside ring of the symmetric group $\text{S}_3$
论文作者
论文摘要
The double Burnside $R$-algebra $\text{B}_R(G,G)$ of a finite group $G$ with coefficients in a commutative ring $R$ has been introduced by S. Bouc.这是$ r $ - 由有限$（g，g）$ - y-modulo a的关系识别不相交联盟和总和。它的繁殖是由张量产物诱导的。 B. Masterson描述$ \ text {b} _ {\ Mathbf {q}}（\ text {s} _3，\ text {s} _3 _3）$作为$ \ Mathbf {q}^{8 \ times 8} $的subalgebra。我们给出了此描述的变体，并继续描述$ \ text {b} _r（\ text {s} _3，\ text {s} _3）$ for $ r \ in \ {\ MathBf {z}，\ MathBf {z} _ {（2）}，\ Mathbf {f} _2，\ \ m athbf {z} _ {（3）}，\ mathbf {f} _3 \} $ r $。
The double Burnside $R$-algebra $\text{B}_R(G,G)$ of a finite group $G$ with coefficients in a commutative ring $R$ has been introduced by S. Bouc. It is $R$-linearly generated by finite $(G,G)$-bisets, modulo a relation identifying disjoint union and sum. Its multiplication is induced by the tensor product. B. Masterson described $\text{B}_{\mathbf{Q}}(\text{S}_3,\text{S}_3)$ as a subalgebra of $\mathbf{Q}^{8\times 8}$. We give a variant of this description and continue to describe $\text{B}_R(\text{S}_3,\text{S}_3)$ for $R\in\{\mathbf{Z},\mathbf{Z}_{(2)},\mathbf{F}_2,\mathbf{Z}_{(3)},\mathbf{F}_3\}$ via congruences as suborders of certain $R$-orders respectively via path algebras over $R$.
