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On the Cohomological Dimension of Soluble Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 24 / Issue 4 / 01 December 1981
- Published online by Cambridge University Press:
- 20 November 2018, pp. 385-392
- Print publication:
- 01 December 1981
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- Article
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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.
