Maximal solvable subgroups

发布时间：2025-08-01 作者：浏览次数：

Speaker:	Mikko Korhonen	DateTime:	2025年8月5日（周二）上午9:55-10:35
Brief Introduction to Speaker: 南方科技大学		Place:	国交2号楼315报告厅
Abstract: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...