### 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) |
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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 |

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### 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