The idea of applying isoperimetric functions to group theory is due to M. Gromov , We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in , , and . Our bicombing is related to but different from the combings defined by M. Bridson . 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.
- 1991 Mathematics subject classification
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