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June 2013 Isomorphism Classes and Zeta-functions of Some Nilpotent Groups
Fumitake HYODO
Tokyo J. Math. 36(1): 163-175 (June 2013). DOI: 10.3836/tjm/1374497517

Abstract

In this article, we study a class of groups which are commensurable with a direct product of the discrete Heisenberg group and a free abelian group, or a free abelian group by using zeta functions of groups defined by Grunewald, Segal, and Smith as generating functions of the number of subgroups of given index $n$. We will show that zeta functions determine their isomorphism classes for groups belonging to the above class.

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Fumitake HYODO. "Isomorphism Classes and Zeta-functions of Some Nilpotent Groups." Tokyo J. Math. 36 (1) 163 - 175, June 2013. https://doi.org/10.3836/tjm/1374497517

Information

Published: June 2013
First available in Project Euclid: 22 July 2013

zbMATH: 1287.20035
MathSciNet: MR3112381
Digital Object Identifier: 10.3836/tjm/1374497517

Rights: Copyright © 2013 Publication Committee for the Tokyo Journal of Mathematics

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Vol.36 • No. 1 • June 2013
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