2011/12/31 by Jokke Häsä · 8 citations
Computer Science · Engineering · Mathematics · #Character (mathematics) #Classification of finite simple groups #Coding theory and cryptography #Combinatorics #Conjugacy class #Degree (music) #Dimension (graph theory) #Finite Group Theory Research #Geometry #Group (periodic table) #Group of Lie type #Group theory #Lie group #Mathematical analysis #Mathematics #Projective representation #Projective test #Pure mathematics #Simple (philosophy) #Simple Lie group #Simple group #Type (biology) #Upper and lower bounds #graph theory and CDMA systems #math.GR #math.RT #msc:20C33
paper · pdf · doi:10.1016/j.jalgebra.2014.02.031
published in Journal of Algebra 407, 275-306 (Elsevier BV)
arxiv created 2013/07/17 · openalex publication_date 2014/04/11 · arxiv updated 2014/07/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we give a bound to the number of conjugacy classes of maximal subgroups of any almost simple group whose socle is a classical group of Lie type. The bound is 2n5.2+nlog2log2 q, where n is the dimension of the classical socle and q is the size of the defining field. To obtain the bound, we first bound the number of projective cross-characteristic representations of simple groups of Lie type as a function of the representation degree. These bounds are computed for different families of groups separately. In the computation, we use information on class numbers, minimal character degrees and gaps between character degrees.