### Abstract

The idea of applying isoperimetric functions to group theory is due to M. Gromov [8], We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.

Original language | English (US) |
---|---|

Pages (from-to) | 515-523 |

Number of pages | 9 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - 1993 |

Externally published | Yes |

### Fingerprint

### Keywords

- 05C25
- 1991 Mathematics subject classification
- 20F05

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*36*(3), 515-523. https://doi.org/10.1017/S0013091500018587

**A bicombing that implies a sub-exponential isoperimetric inequality.** / Huck, Günther; Stephan Rosebrock, S. R.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 36, no. 3, pp. 515-523. https://doi.org/10.1017/S0013091500018587

}

TY - JOUR

T1 - A bicombing that implies a sub-exponential isoperimetric inequality

AU - Huck, Günther

AU - Stephan Rosebrock, S. R.

PY - 1993

Y1 - 1993

N2 - The idea of applying isoperimetric functions to group theory is due to M. Gromov [8], We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.

AB - The idea of applying isoperimetric functions to group theory is due to M. Gromov [8], We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.

KW - 05C25

KW - 1991 Mathematics subject classification

KW - 20F05

UR - http://www.scopus.com/inward/record.url?scp=84972054526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972054526&partnerID=8YFLogxK

U2 - 10.1017/S0013091500018587

DO - 10.1017/S0013091500018587

M3 - Article

AN - SCOPUS:84972054526

VL - 36

SP - 515

EP - 523

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -