Gang Chen

Central China Normal University · School of Mathematics and Statistics

For any finite group 𝐺 and a positive integer 𝑚, we define and study a Schur ring over the direct power G m G^{m} , which gives an algebraic interpretation of the partition of G m G^{m} obtained by the 𝑚-dimensional Weisfeiler–Leman algorithm. It is proved that this ring determines the group 𝐺 up to isomorphism if m ≥ 3 m\geq 3 , and approaches the...

Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved.

In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They are generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then classify those which are non-degenerate or symmetric. Finally, we classify such fusion categories of rank 4.

A Cartesian decomposition of a coherent configuration \({\cal X}\) is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of \({\cal X}\) comes from a certain Cartesian decomposition. It is proved that if the coherent configuration \({\cal X}\) is thick,...

In this paper, we study fusion categories which contain a proper fusion subcategory with maximal rank. They can be viewed as generalizations of near-group fusion categories. We first prove that they admit spherical structure. We then classify those which are non-degenerate or symmetric. Finally, we classify such fusion categories of rank 4.

Recent classification of 3/2-transitive permutation groups leaves us with three infinite families of groups which are neither 2-transitive, nor Frobenius, nor one-dimensional affine. The groups of the first two families correspond to special actions of PSL(2, q) and PΓL(2, q), whereas those of the third family are the affine solvable subgroups of A...

A Cartesian decomposition of a coherent configuration $\cal X$ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of $\cal X$ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration $\cal X$ is thick, then there i...

For the direct product Z×Z3 of infinite cyclic group Z and a cyclic group Z3 of order 3, the Schur rings over it are classified. In particular, all the Schur rings are proved to be traditional.

The schurity of association schemes has been studied in many papers. One of the major topics is to investigate the schurity of those association schemes whose thin residues are thin. A difficult case is that the thin residue is an elementary abelian p-group of rank 2. A class of these association schemes has played an important role in the study of...

For the direct product $\cZ\times \cZ_3$ of infinite cyclic group $\cZ$ and a cyclic group $\cZ_3$ of order $3$, the schur rings over it are classified. In particular, all the schur rings are proved to be traditional.

Recent classification of $\frac{3}{2}$-transitive permutation groups leaves us with three infinite families of groups which are neither $2$-transitive, nor Frobenius, nor one-dimensional affine. The groups of the first two families correspond to special actions of ${\mathrm{PSL}}(2,q)$ and ${\mathrm{P\Gamma L}}(2,q),$ whereas those of the third fam...