关于p-可除kG-模的一些结论（英文）  

SOME RESULTS ON THE p-DIVISIBLE kG-MODULE

作　　者：黄文林[1] 

机构地区：[1]中国人民大学信息学院,北京100872

出　　处：《数学杂志》2017年第3期613-620,共8页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10826057)

摘　　要：本文研究了p-可除kG-模,这是一类由群阶的素数因子来控制的模类.利用Heller算子,证明了n次Heller算子置换非投射不可分解p-可除kG-模的同类;利用模的诱导和限制方法,证明了若H是G的强p-嵌入子群,则Green对应建立了不可分解p-可除kG-模的同构类与不可分解p-可除kH-模的同构类之间的一一对应.推广了不可分解相对投射kG-模上的Green对应.In this paper, we study the p-divisible kG-module, which is essentially controlled by the prime p. With the Heller operator, we prove that the nth-Heller operator permutates the isomorphism classes of the indecomposable non-projective p-divisible kG-modules; and with the methods of induction and restriction, we prove that Green correspondence induces a bijection between the isomorphism classes of the indecomposable p-divisible kG-modules and that of the in- decomposable p-divisible kH-modules whenever H is strongly p-embedded in G, which generalizes Green correspondence for the indecomposable relative projective modules.

关 键 词：p-可除kG-模 置换模 Heller算子 Green对应 

分 类 号：O152.1[理学—数学] O152.6[理学—基础数学]