## Tokyo Journal of Mathematics

### Isomorphism Classes and Zeta-functions of Some Nilpotent Groups

Fumitake HYODO

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 163-175.

Dates
First available in Project Euclid: 22 July 2013

https://projecteuclid.org/euclid.tjm/1374497517

Digital Object Identifier
doi:10.3836/tjm/1374497517

Mathematical Reviews number (MathSciNet)
MR3112381

Zentralblatt MATH identifier
1287.20035

#### Citation

HYODO, Fumitake. Isomorphism Classes and Zeta-functions of Some Nilpotent Groups. Tokyo J. Math. 36 (2013), no. 1, 163--175. doi:10.3836/tjm/1374497517. https://projecteuclid.org/euclid.tjm/1374497517

#### References

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