FREE ACTION OF FINITE GROUPS ON SPACES OF COHOMOLOGY TYPE (0, b)

SINGH, K. SOMORJIT ; SINGH, HEMANT KUMAR ; SINGH, TEJ BAHADUR

Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 673-680

Résumé

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.

Détail

DOI : 10.1017/S0017089517000362

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