@article{b0843bf2014f44e5b7cbeadb34da4f5a,

title = "A bicombing that implies a sub-exponential isoperimetric inequality",

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.",

keywords = "05C25, 1991 Mathematics subject classification, 20F05",

author = "G{\"u}nther Huck and {Stephan Rosebrock}, {S. R.}",

note = "Funding Information: This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (Grant no. 12213084) and the Smoking Research Foundation (K.S.). We appreciate Drs. T. Kanzaki and N. Koide (Okayama University School of Medicine), Y. Kusaka (Kusaka Hospital, Bizen, Okayama), S. Hamanishi and E. Senoh (Junpukai Health Maintenance Center, Okayama) for their generous help in this study. Funding Information: Acknowledgments. This work was supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (Grant no. 12213084) and the Smoking Research Foundation (K.S.). We appreciate Drs. T. Kanzaki and N. Koide (Okayama University School of Medicine), Y. Kusaka (Kusaka Hospital, Bizen, Okayama), S. Hamanishi and E. Senoh (Junpukai Health Maintenance Center, Okayama) for their generous help in this study.",

year = "1993",

doi = "10.1017/S0013091500018587",

language = "English (US)",

volume = "36",

pages = "515--523",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

number = "3",

}