2007/07/24 by Zeng Jiwen, Jiwen, Zeng
Computer Science · Engineering · Mathematics · #20c20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems #math.GR #math.RT #msc:20c20
paper · pdf · doi:10.48550/arxiv.0707.3495
16 pages, changed contents and title
openalex publication_date 2007/07/24 · arxiv created 2008/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group and N be a normal subgroup of G. Let J=J(F[N]) denote the Jacboson radical of F[N] and I=\rm Ann(J)=\α∈ F[G]|Jα=0\. We have another algebra F[G]/I. We study the decomposition of Cartan matrix of F[G] according to F[G/N] and F[G]/I. This decomposition establishs some connections between Cartan invariants and chief composition factors of G. We find that existing zero-defect p-block in N depends on the properties of I in F[G] or Cartan invariants. When we consider the Cartan invariants for a block algebra B of G, the decomposition is related to what kind of blocks in N covered by B. We mainly consider a block B of G which covers a block b of N with l(b)=1. In two cases, we prove Willems' conjecture holds for these blocks, which covers some true cases by Holm and Willems. Furthermore We give an affirmative answer to a question by Holm and Willems in our cases. Some other results about Cartan invariants are presented in our paper.