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

### Volume 66 / 2018

Bulletin Polish Acad. Sci. Math. 66 (2018), 167-177
MSC: Primary 57S17; Secondary 57S25.
DOI: 10.4064/ba8150-9-2018
Published online: 28 September 2018

#### Abstract

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 $G=A_5\times C_p$, where $p=3,5,7$, we present a strategy of excluding smooth effective one fixed point $G$-actions on low-dimensional spheres.