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2015 | 13 | 1 |
Tytuł artykułu

Two bounds on the noncommuting graph

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Erdős introduced the noncommuting graph in order to study the number of commuting elements in a finite group. Despite the use of combinatorial ideas, his methods involved several techniques of classical analysis. The interest for this graph has become relevant during the last years for various reasons. Here we deal with a numerical aspect, showing for the first time an isoperimetric inequality and an analytic condition in terms of Sobolev inequalities. This last result holds in the more general context of weighted locally finite graphs.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
zaakceptowano
2014-03-07
otrzymano
2014-08-11
online
2015-04-15
Twórcy
  • Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149,
    Centro de Tecnologia, Bloco C, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909, Rio de Janeiro, Brasil
  • Department of Mathematics and Applied Mathematics, University of Cape Town,
    Private Bag X1, Rondebosch 7701, Cape Town, South Africa
Bibliografia
  • [1] Abdollahi A., Akbari S., Maimani H.R., Non-commuting graph of a group, J. Algebra, 2006, 298, 468–492
  • [2] Ambrosio L., Gigli N., Mondino A., Rajala T., Riemannian Ricci curvature lower bounds in metric measure spaces with σ–finitemeasure, Trans. Amer. Math. Soc. (in press), preprint available at http://arxiv.org/pdf/1207.4924v2.pdf
  • [3] Ambrosio L., Mondino A., Savaré G., On the Bakry–Émery condition, the gradient estimates and the Local–to–Global property ofRCD*(k, n) metric measure spaces, J. Geom. Anal. (in press), preprint available at http://arxiv.org/pdf/1309.4664v1.pdf
  • [4] Aubin T., Nonlinear analysis on manifolds: Monge–Ampére equations, Grundlehren der Mathematischen Wissenschaften, 252,Springer, Berlin, 1982
  • [5] Bakry D., Coulhon T., Ledoux M., Saloff–Coste L., Sobolev inequalities in disguise, Indiana Univ. Math. J., 1995, 44, 1033–1074
  • [6] Chung F.R.K., Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 92, AMS publications, New York, 1996
  • [7] Chung F.R.K., Grigor’yan A., Yau S.T., Higher eigenvalues and isoperimetric inequalities on riemannian manifolds and graphs,Comm. Anal. Geom., 2000, 8, 969–1026
  • [8] Chung F.R.K., Discrete isoperimetric inequalities, In: Surveys in differential geometry, Vol. IX, Int. Press, Somerville, MA, 2004,53–82
  • [9] Darafsheh M.R., Groups with the same non-commuting graph, Discrete Appl. Math., 2009, 157, 833–837[WoS]
  • [10] Hebey E., Nonlinear analysis on manifolds: Sobolev spaces and inequalities, Courant Lecture Notes in Mathematics, Vol.5, NewYork University Courant Institute of Mathematical Sciences, New York, 1999
  • [11] Hofmann K.H., Russo F.G., The probability that x and y commute in a compact group, Math. Proc. Cambridge Phil. Soc., 2012,153, 557–571[WoS]
  • [12] Hofmann K.H., Russo F.G., The probability that xm and yn commute in a compact group, Bull. Aust. Math. Soc., 2013, 87, 503–513[WoS]
  • [13] Moghaddamfar A.R., About noncommuting graphs, Siberian Math. J., 2005, 47, 1112–1116
  • [14] Mondino A., Nardulli S., Existence of isoperimetric regions in noncompact riemannian manifolds under Ricci or scalar curvatureconditions, Comm. Anal. Geom., preprint available at http://arxiv.org/pdf/1210.0567v1.pdf
  • [15] Nardulli S., The isoperimetric profile of a noncompact Riemannian manifold for small volumes, Calc. Var. PDE, 2014, 49, 173–195
  • [16] Neumann B.H., A problem of Paul Erd˝os on groups, J. Aust. Math. Soc., 1976, 21, 467–472
  • [17] Russo F.G., Problems of connectivity between the Sylow graph, the prime graph and the non-commuting graph of a group, Adv.Pure Math., 2012, 2, 373–378
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0027
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