Two bounds on the noncommuting graph

Stefano Nardulli; Francesco G. Russo

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Stefano Nardulli, and Francesco G. Russo. "Two bounds on the noncommuting graph." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/271038>.

@article{StefanoNardulli2015,
abstract = {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.},
author = {Stefano Nardulli, Francesco G. Russo},
journal = {Open Mathematics},
keywords = {Noncommuting graph; Sobolev–Poincaré inequality; Laplacian operator; Isoperimetric inequality},
language = {eng},
number = {1},
pages = {null},
title = {Two bounds on the noncommuting graph},
url = {http://eudml.org/doc/271038},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Stefano Nardulli
AU - Francesco G. Russo
TI - Two bounds on the noncommuting graph
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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.
LA - eng
KW - Noncommuting graph; Sobolev–Poincaré inequality; Laplacian operator; Isoperimetric inequality
UR - http://eudml.org/doc/271038
ER -

References

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  12. [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] Zbl1271.22002
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  14. [14] Mondino A., Nardulli S., Existence of isoperimetric regions in noncompact riemannian manifolds under Ricci or scalar curvature conditions, Comm. Anal. Geom., preprint available at http://arxiv.org/pdf/1210.0567v1.pdf Zbl06610800
  15. [15] Nardulli S., The isoperimetric profile of a noncompact Riemannian manifold for small volumes, Calc. Var. PDE, 2014, 49, 173–195 Zbl1293.49107
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