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FREE ACTION OF FINITE GROUPS ON SPACES OF COHOMOLOGY TYPE (0, b)
Published online by Cambridge University Press: 28 January 2018
Abstract
Let G be a finite group acting freely on a finitistic space X having cohomology type (0, b) (for example, $\mathbb S$n ×
$\mathbb S$2n is a space of type (0, 1) and the one-point union
$\mathbb S$n ∨
$\mathbb S$2n ∨
$\mathbb S$3n is a space of type (0, 0)). It is known that a finite group G that contains ℤp ⊕ ℤp ⊕ ℤp, p a prime, cannot act freely on
$\mathbb S$n ×
$\mathbb S$2n. In this paper, we show that if a finite group G acts freely on a space of type (0, 1), where n is odd, then G cannot contain ℤp ⊕ ℤp, p an odd prime. For spaces of cohomology type (0, 0), we show that every p-subgroup of G is either cyclic or a generalized quaternion group. Moreover, for n even, it is shown that ℤ2 is the only group that can act freely on X.
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- Type
- Research Article
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- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2018
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