有限群的Green环上Adams运算的周期性
Periodicity of Adams operations on the Green ring of a finite group
摘要：
域$K$上的群$G$的Green环上的Adams运算$ψ_Λ^n$和$ψ_S^n$为研究$KG$ -模的外幂和对称幂提供了一个框架.当$G$是有限的且$K$具有素特征$p$时，我们证明了$ψ_Λ^n$和$ψ_S^n$在$n$中是周期的当且仅当$G$的Sylow $p$ -子群是循环的.在$G$是一个循环的$p$ -组的情况下，我们找到的最小周期，并使用西蒙兹最近的工作来表达$ψ_S^n$的$ψ_Λ^n$。
英文摘要：
The Adams operations $ψ_Λ^n$ and $ψ_S^n$ on the Green ring of a group $G$ over a field $K$ provide a framework for the study of the exterior powers and symmetric powers of $KG$-modules. When $G$ is finite and $K$ has prime characteristic $p$ we show that $ψ_Λ^n$ and $ψ_S^n$ are periodic in $n$ if and only if the Sylow $p$-subgroups of $G$ are cyclic. In the case where $G$ is a cyclic $p$-group we find the minimum periods and use recent work of Symonds to express $ψ_S^n$ in terms of $ψ_Λ^n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
