Editor-in-Chief: Wilson, John S.
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Citation Information: Journal of Group Theory. Volume 10, Issue 2, Pages 245–266, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2007.020, April 2007
Let Γ be a group which is an extension of ℤ2 by ℤ, where the action of ℤ on ℤ2 is given by a structure matrix of the form
for some integer k ≥ 2. The group Γ is generated by the set S which consists of the standard basis of ℤ2 together with a generator of ℤ. We prove that the growth series of Γ with respect to the generating set S is a rational function and we explicitly compute it in terms of k.
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