Geodesic
FREE ACTION OF FINITE GROUPS ON SPACES OF COHOMOLOGY TYPE (0, b)
Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 673-680

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DOI

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. 
SINGH, K. SOMORJIT; SINGH, HEMANT KUMAR; SINGH, TEJ BAHADUR. FREE ACTION OF FINITE GROUPS ON SPACES OF COHOMOLOGY TYPE (0, b). Glasgow mathematical journal, Tome 60 (2018) no. 3, pp. 673-680. doi: 10.1017/S0017089517000362
@article{10_1017_S0017089517000362,
     author = {SINGH, K. SOMORJIT and SINGH, HEMANT KUMAR and SINGH, TEJ BAHADUR},
     title = {FREE {ACTION} {OF} {FINITE} {GROUPS} {ON} {SPACES} {OF} {COHOMOLOGY} {TYPE} (0, b)},
     journal = {Glasgow mathematical journal},
     pages = {673--680},
     year = {2018},
     volume = {60},
     number = {3},
     doi = {10.1017/S0017089517000362},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089517000362/}
}
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