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 |
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Keywords
- 05C25
- 1991 Mathematics subject classification
- 20F05
ASJC Scopus subject areas
- Mathematics(all)
Cite this
A bicombing that implies a sub-exponential isoperimetric inequality. / Huck, Günther; Stephan Rosebrock, S. R.
In: Proceedings of the Edinburgh Mathematical Society, Vol. 36, No. 3, 1993, p. 515-523.Research output: Contribution to journal › Article
}
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
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 -