Geodesic
On the Cohomological Dimension of Soluble Groups
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 385-392

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

It is known that every torsion-free soluble group G of finite Hirsch number hG is countable, and its homological and cohomological dimensions over the integers and rationals satisfy the inequalities We prove that G must be finitely generated if the equality hG = cdQG holds. Moreover, we show that if G is a countable soluble group of finite Hirsch number, but not necessarily torsion-free, and if hG = cdQG, then hḠ = cdQḠ for every homomorphic image Ḡ of G.
DOI : 10.4153/CMB-1981-060-x
Mots-clés : 0014, 0015, soluble groups, Hirsch numbers, homological and cohomological dimension 
Gildenhuys, D.; Strebel, R. On the Cohomological Dimension of Soluble Groups. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 385-392. doi: 10.4153/CMB-1981-060-x
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