%0 Journal Article
%T Periodicity of Adams operations on the Green ring of a finite group
%A R. M. Bryant
%A Marianne Johnson
%J Mathematics
%D 2009
%I arXiv
%X The Adams operations $\psi_\Lambda^n$ and $\psi_S^n$ 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 $\psi_\Lambda^n$ and $\psi_S^n$ 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 $\psi_S^n$ in terms of $\psi_\Lambda^n$.
%U http://arxiv.org/abs/0912.2933v1