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Periodicity of Adams operations on the Green ring of a finite group | R. M. Bryant
; Marianne Johnson
; | Date: |
15 Dec 2009 | Abstract: | 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 $psi_Lambda^n$. | Source: | arXiv, 0912.2933 | Services: | Forum | Review | PDF | Favorites |
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