Homotopy fixed point set for $p$-compact toral group
Bull. Korean Math. Soc. 2001 Vol. 38, No. 1, 143-148
Hyang-Sook Lee
Ewha Women's University
Abstract : First, we show the finiteness property of the homotopy fixed point set of $p$-discrete toral group. Let $G_{\infty}$ be a $p$-discrete toral group and $X$ be a finite complex with an action of $G_{\infty}$ such that $X^{K}$ is nilpotent for each finite $p$-subgroup $K$ of $G_{\infty}$. Assume $X$ is ${\mathbb F}_p$-complete. Then $X^{hG_{\infty}}$ is ${\mathbb F}_p$-finite. Using this result, we give the condition so that $X^{hG}$ is ${\mathbb F}_p$-finite for $p$-compact toral group $G$.
Keywords : homotopy fixed point set, $p$-compact toral group
MSC numbers : 55M20, 57S20, 55P91
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