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 Homotopy fixed point set of the homotopy fibre Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 755-762 Hyang-Sook Lee Ewha Womans University Abstract : Let ${\mathcal X}$ be a $p$-compact group, ${\mathcal Y} \to {\mathcal X}$ be a $p$-compact subgroup of ${\mathcal X}$ and $G \to {\mathcal X}$ be a $p$-compact toral subgroup of ${\mathcal X}$ with $({\mathcal X}/{\mathcal Y})^{hG} \neq \emptyset$. In this paper we show that the homotopy fixed point set of the homotopy fibre $({\mathcal X}/{\mathcal Y})^{hG}$ is ${\mathbb F}_p$-finite. Keywords : $p$-compact group, loop space, homotopy fixed point set MSC numbers : Primary 55R35, Secondary 55P35 Downloads: Full-text PDF