Journal of Group Theory
Editor-in-Chief: Parker, Christopher W. / Wilson, John S.
Managing Editor: Howie, James / Khukhro, Evgenii I. / Kramer, Linus
IMPACT FACTOR increased in 2015: 0.505
SCImago Journal Rank (SJR) 2015: 0.748
Source Normalized Impact per Paper (SNIP) 2015: 0.849
Impact per Publication (IPP) 2015: 0.412
Mathematical Citation Quotient (MCQ) 2015: 0.45
The mean Dehn functions of abelian groups
1 O. Bogopolski, Institute of Mathematics, Koptjuga 4, Novosibirsk, 630090, Russia, and Universität Dortmund, Fachbereich Mathematik, Lehrstuhl VI (Algebra), Vogelpothsweg 87, 44221 Dortmund, Germany. E-mail: (email)
2 E. Ventura, Dept. Mat. Apl. III, Univ. Pol. Catalunya, Barcelona, Spain, and Centre de Recerca Matemàtica, Barcelona, Spain. E-mail: (email)
Citation Information: Journal of Group Theory. Volume 11, Issue 4, Pages 569–586, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2008.035, July 2008
- Published Online:
While Dehn functions D(n) of finitely presented groups have been well studied in the literature, mean Dehn functions have received less attention. Gromov introduced the notion of the mean Dehn function D mean(n) of a group, suggesting that in many cases it should grow more slowly than the Dehn function itself This paper presents computations pointing in this direction. In the case of any finite presentation of an infinite finitely generated abelian group (for which it is well known that D(n) ~ n 2 except in the 1-dimensional case), we show that the three variants D osmean(n), D smean(n) and D mean(n) all are bounded above by Kn(In n)2, where the constant K depends only on the presentation (and the geodesic combing) chosen. This improves an earlier bound given by Kukina and Roman'kov.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.