## Title data

Stoll, Michael:

**Rational and transcendental growth series for the higher Heisenberg groups.**

*In:* Inventiones Mathematicae.
Vol. 126
(1996)
Issue 1
.
- pp. 85-109.

ISSN 1432-1297

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 |
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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 (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - 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: | 15 Sep 2022 12:15 |

URI: | https://eref.uni-bayreuth.de/id/eprint/7989 |