论文标题
有限群和欧拉特征的子组晶格的Möbius函数
Möbius function of the subgroup lattice of a finite group and Euler Characteristic
论文作者
论文摘要
Hall引入了有限组的子组晶格的Möbius函数，并申请研究几个问题。 In this paper, we consider the Möbius function defined on an order ideal related to the lattice of the subgroups of an irreducible subgroup $G$ of the general linear group $\mathrm{GL}(n,q)$ acting on the $n$-dimensional vector space $V=\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the有限字段，$ q $元素。我们发现此功能与两个Simplicial Complextes $δ_1$和$δ_2$的Euler特征之间的关系，前者是从$ V $的子空间的晶格中升起的，后者是从$ G $的子组晶格中的。
The Möbius function of the subgroup lattice of a finite group has been introduced by Hall and applied to investigate several questions. In this paper, we consider the Möbius function defined on an order ideal related to the lattice of the subgroups of an irreducible subgroup $G$ of the general linear group $\mathrm{GL}(n,q)$ acting on the $n$-dimensional vector space $V=\mathbb{F}_q^n$, where $\mathbb{F}_q$ is the finite field with $q$ elements. We find a relation between this function and the Euler characteristic of two simplicial complexes $Δ_1$ and $Δ_2$, the former raising from the lattice of the subspaces of $V$, the latter from the subgroup lattice of $G$.
