Special Blocks of Finite Groups  

作　　者：Ji Ping ZHANG 

机构地区：[1]Beijing International Center for Mathematical Research Lmam, School of Mathematical Sciences,Peking University

出　　处：《Acta Mathematica Sinica,English Series》2016年第1期115-123,共9页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11131001,11201008)

摘　　要：We first determine in this paper the structure of the generalized Fitting subgroup F＊ （G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to either a Sylow p-subgroup or a fixed p-subgroup of G. Then we prove that if a finite group L acts transitively on the set of its proper Sylow p-intersections, then either L/Op（L） has a T.I. Sylow p-subgroup or p = 2 and the normal closure of a Sylow 2-subgroup of L/O2（L） is 2-nilpotent with completely descripted structure. This solves a long-open problem. We also obtain some generalizations of the classic results by Isaacs and Passman on half-transitivity.We first determine in this paper the structure of the generalized Fitting subgroup F＊ （G） of the finite groups G all of whose defect groups （of blocks） are conjugate under the automorphism group Aut（G） to either a Sylow p-subgroup or a fixed p-subgroup of G. Then we prove that if a finite group L acts transitively on the set of its proper Sylow p-intersections, then either L/Op（L） has a T.I. Sylow p-subgroup or p = 2 and the normal closure of a Sylow 2-subgroup of L/O2（L） is 2-nilpotent with completely descripted structure. This solves a long-open problem. We also obtain some generalizations of the classic results by Isaacs and Passman on half-transitivity.

关 键 词：Finite groups REPRESENTATIONS BLOCKS defect groups 

分 类 号：O152.1[理学—数学] O152[理学—基础数学]