报告题目：Some invariants of representations for the generalized…

报 告 人：刘杰

时 间：2025年8月5日（周二）下午15:15-15:55

地 点：国交2号楼315报告厅

简 介：Since it is impossible to classify all the representations of the generalized Kronecker quiver K(n), it is desirable to find the invariants. Claus Ringel introduces two invariants for its covering T(n): center and radius, and he wants to know what would happen if we use the reflection functor to act on them. In this talk, we answer his question and we classify the elementary representations of K(n). Moreover, we follow Carlson, Friedlander and Pevtsova’s definition of modules of constant Jordan type, and we show that there are only two types of modules of constant Jordan type in the regular component of T(n).

报告题目：Union of products of subgroups in finite groups

报 告 人：孟沆洋

时 间：2025年8月5日（周二）下午14:30-15:10

地 点：国交2号楼315报告厅

简 介：In this talk, we will introduce some interesting results about the union of two products of subgroups. Let G be a finite group and A，B，C be subgroups of G. We prove that if G is the union of AB and BC, then G = AB or G = BC. But if G is the union of BA and BC, we can not obtain that G = BA or G = BC in general. We also prove that if G is a 2-decomposed group, and G is a Sylow tower group or G is nilpotent-by-nilpotent, then G = BA ∪ BC implies that G = BA or G = BC. This is a joint work with Adolfo Ballester-Bolinches and Gil Kaplan.

报告题目：Maximal solvable subgroups

报 告 人：Mikko Korhonen

时 间：2025年8月5日（周二）上午9:55-10:35

地 点：国交2号楼315报告厅

简 介：A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. In his 1870 Traité, Jordan gave a classification of the maximal solvable subgroups of symmetric groups. The classification reduces to the primitive case, which is equivalent to the problem of classifying maximal irreducible solvable subgroups of GL(d,p), where p is a prime. In GL(d,p), the problem is reduced to the case of primitive irreducible solvable subgroups. These subgroups are then constructed in terms of maximal irreducible solvable subgroups of general symplectic groups GSp(2k,r) (r prime) and orthogonal groups O^±(2k,2). In this talk, we will discuss Jordan's classification in modern terms. More generally, we consider the complete classification of maximal irreducible solvable subgroups of classical groups such as GL(n,q), GSp(n,q), and GO(n,q), where q is a power of a prime. From the classification we also get a recursive construction of the maximal irreducible solva...