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On the Cohomological Dimension of Soluble Groups

Published online by Cambridge University Press:  20 November 2018

D. Gildenhuys  and
R. Strebel
D. Gildenhuys
Affiliation:
Department of Mathematics, McGill UniversityBurnside HallMontreal, PQ, Canada H3A 2K6
R. Strebel
Affiliation:
Department of Mathematics, University of IllinoisUrbana, Illinois 61801
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Abstract

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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.

Keywords

00140015soluble groupsHirsch numbershomological and cohomological dimension
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 4 , 01 December 1981 , pp. 385 - 392
Copyright
Copyright © Canadian Mathematical Society 1981

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