关于有限群的直积的标号表
On the Table of Marks of a Direct Product of Finite Groups
摘要：
给出了计算有限群的直积的标号表的一种方法。与两个有限群的直积的特征标表不同，它的标号表不是两个群的标号表的Kronecker积。基于直积作为三个较小偏序的关系积在子群格上的包含序的分解，我们把直积的标号表本质上描述为三类关联矩阵的矩阵积.这些矩阵中的每一个又被描述为稀疏分块对角矩阵。作为应用，我们利用这个矩阵积的一个变形构造了对称群$S_3$的有理双Burnside代数的一个鬼环和一个标记同态.
英文摘要：
We present a method for computing the table of marks of a direct product of finite groups. In contrast to the character table of a direct product of two finite groups, its table of marks is not simply the Kronecker product of the tables of marks of the two groups. Based on a decomposition of the inclusion order on the subgroup lattice of a direct product as a relation product of three smaller partial orders, we describe the table of marks of the direct product essentially as a matrix product of three class incidence matrices. Each of these matrices is in turn described as a sparse block diagonal matrix. As an application, we use a variant of this matrix product to construct a ghost ring and a mark homomorphism for the rational double Burnside algebra of the symmetric group~$S_3$.
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