Geodesic
Some remarks on the p-homotopy type of B∑p2
Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 337-342

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite group, H a copy of its p-Sylow subgroup, and N the normalizer of H in G. A theorem by Nishida [10] states the p-homotopy equivalence of suitable suspensions of BN and BG when H is abelian. Recently, in [3] the authors proved a stronger result: let ΩkH be the subgroup of H generated by elements of order pk or less; ifthen BN and BG are stably p-homotopy equivalent. The hypothesis above is obviously verified when H is abelian. In the same paper the authors recall that H does not verify such condition when p = 2 and G = SL2(Fq) for a suitable odd prime power q; in this case BG and BN are not stably 2-homotopy equivalent. 
Brunetti, Maurizio. Some remarks on the p-homotopy type of B∑p2. Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 337-342. doi: 10.1017/S0017089500031761
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