Actions of elementary 𝑝-groups on manifolds

Abstract

Introduction. An elementary p-group of rank k will be a group isomorphic to k copies of Zp (the additive group of integers modulo a prime p). Smith In the first part of this paper we establish a result which states that given a compact manifold X of dimension n, the sum of whose mod p Betti numbers is an integer B, there exists an integer N(n, B), depending only upon n and B, such that no elementary p-group of rank greater than JV can operate effectively on X.