本项目将研究几类与有限群有关的组合结构即相干配置(Coherent Configuration)的可分性和Schur性问题， 这两个问题在代数组合领域受到了广泛的关注。第一，研究定义在两类特殊有限群的直积上的齐次凯莱相干配置的可分性问题(这类相干配置的Schur性问题已得到很好了研究)。 第二， 从一个阶为$p^3$的超特殊$p$-群和这个群在一个特征不为$p$的有限域上的一个维数为$p$的不可约模出发， 构造一个和这个群的表示密切相关的“超特殊”-齐次相干配置，我们将研究这类相干配置的可分性。 第三， 研究有限群的$k$-S-环和$k$特征标理论， 研究有限群的4-S-环的代数同构类。 第四， 研究拟-正则的相干配置的齐次成份个数为4时， 这个相干配置的可分性以及一般的拟-正则相干配置的可分性和Schur性。

In this project, we will study the separability problem and schurity problem for some classes of coherent configruations which are related to finite groups. These problems are studied extensively in the area of algebraic combinatorics. First, study the separability problem for a class of Cayley schemes which are defined over the direct product of two special classes of finite groups( the schurity problem for these schemes are well studied). Second, for an extralspecial $p$-group $G$ of order $p^3$, take an irreducible module $V$ with dimension $p$ of $G$ over a finite field of characteristic different from $p$. We can construct an extraspeical scheme which is related to the representation of the finite group $G$. We will study the separability problem for these kind of schemes. Third, we will study the $k$-S-ring and $k$-characters of a finite group and the algebraic isomorphic class of 4-S-ring of a finite group. Fourth, we will study the separability problem for quasi-regular coherent configurations with number of fibers equal 4. In addition, we will study the separability problem and the schurity problem for arbitrary quasi-regular coherent configurations.