A note on homotopy types of connected components of

Gottlieb has shown that connected components of are the classifying spaces of gauge groups of principal -bundles over S4. Tsukuda has investigated the homotopy types of connected components of . But unfortunately, his proof is not complete for p=2. In this paper, we give a complete proof. Moreover, we investigate the further divisibility of ϵi defined in Tsukuda’s paper. We apply this to classification problem of gauge groups as An-spaces.