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Rational and transcendental growth series for the higher Heisenberg groups

Title data

Stoll, Michael:
Rational and transcendental growth series for the higher Heisenberg groups.
In: Inventiones Mathematicae. Vol. 126 (September 1996) Issue 1 . - pp. 85-109.
ISSN 0020-9910
DOI: https://doi.org/10.1007/s002220050090

Project information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

This paper considers growth series of 2-step nilpotent groups with infinite cyclic derived subgroup. Every such group G has a subgroup of finite index of the form H n ×ℤm , where H_n is the discrete Heisenberg group of length 2n+1. We call n the Heisenberg rank of G.

We show that every group of this type has some finite generating set such that the corresponding growth series is rational. On the other hand, we prove that if G has Heisenberg rank n ≧ 2, then G possesses a finite generating set such that the corresponding growth series is a transcendental power series.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: The author thanks the Deutsche Forschungsgemeinschaft for supporting the present work by a research grant.
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 10 Mar 2015 15:22
Last Modified: 10 Mar 2015 15:22
URI: https://eref.uni-bayreuth.de/id/eprint/7989