Finite Group actions on Spheres.

The unit spheres in orthogonal  representations of finite groups give  basic linear examples of group actions on spheres. The talk will be about the connection between finite group theory, and the fixed sets and isotropy subgroups found in actions on spheres. For example, there are finite groups which act freely and smoothly on spheres, but not linearly. The complexity of non-free actions can be measured by the rank of the isotropy subgroups. I will survey previous results and describe my