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Nonexistence of smooth effective one fixed point action of finite Oliver groups on low-dimensional spheres

Borowiecka A., Mizerka P.

Bulletin of the Polish Academy of Sciences. Mathematics

2018

Vol. 66, no. 2

167--177

According to Laitinen and Morimoto (1998), a finite group G has a smooth effective one fixed point action on some sphere if and only if G is an Oliver group. For some finite Oliver groups G of order up to 216, and for G = A5 x Cp, where p = 3, 5, 7, we present a strategy of excluding smooth effective one fixed point G-actions on low-dimensional spheres.