We consider a purely algebraic result. Then given a circle or cyclic group of
prime order action on a manifold, we will use it to estimate the lower bound of
the number of fixed points. We also give an obstruction to the existence of
$\mathbb{Z}_p$ action on manifolds with isolated fixed points when $p$ is a
prime.Comment: 7 pages, revised slightly to update a new reference and reassign the
  credit of the idea in this not

Li, Ping