Elementary Abelian Group Actions on a Product of Spaces of Cohomology Type (a, b)

Abstract

Let Xn be a finite CW complex with cohomology type (a, b), characterized by an integer n > 1 [20]. In this paper, we show that if G = (Z2)^q acts freely on the product Y =  Xn^i (i from 1 to m) , where Xn^i are finite CW complexes with cohomology type (a, b), a and b are even for every i, then q ≤ m. Moreover, for n even and a = b = 0, we prove that G = (Z2)^q (q ≤ m) is the only finite group which can act freely on Y . These are generalizations of the results which says that the rank of a group acting freely on a space with cohomology type (a, b) where a and b are even, is one and for n even, G = Z2 is the only finite group which acts freely on spaces of cohomology type (0, 0) [17].