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| 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. |
| 关键词: p-可除kG-模 置换模 Heller算子 Green对应 |
| DOI： |
| 分类号:O152.1;O152.6 |
| 基金项目:Supported by National Natural Science Foundation of China (10826057). |
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| SOME RESULTS ON THE p-DIVISIBLE kG-MODULE |
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HUANG Wen-lin
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| Abstract: |
| 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 indecomposable p-divisible kH-modules whenever H is strongly p-embedded in G, which generalizes Green correspondence for the indecomposable relative projective modules. |
| Key words: p-divisible module endo-p-permutation module Heller operator Green correspondence |
