%0 Journal Article %T On an algebraic formula and applications to group action on manifolds %A Ping Li %A Kefeng Liu %J Mathematics %D 2011 %I arXiv %X 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. %U http://arxiv.org/abs/1106.0147v2