Carregant...
Carregant...

Vés al contingut (premeu Retorn)

Degree of commutativity of infinite groups

Autor
Antolin, Y.; Martino, A.; Ventura, E.
Tipus d'activitat
Article en revista
Revista
Proceedings of the American Mathematical Society
Data de publicació
2016-11-16
Volum
145
Número
2
Pàgina inicial
479
Pàgina final
485
DOI
https://doi.org/10.1090/proc/13231 Obrir en finestra nova
Projecte finançador
Métodos geométricos en teoría de grupos
Repositori
http://hdl.handle.net/2117/101873 Obrir en finestra nova
https://arxiv.org/abs/1511.07269 Obrir en finestra nova
Resum
We prove that, in a finitely generated residually finite group of subexponential growth, the proportion of commuting pairs is positive if and only if the group is virtually abelian. In particular, this covers the case where the group has polynomial growth (i.e., virtually nilpotent groups, where the hypothesis of residual finiteness is always satisfied). We also show that, for non-elementary hyperbolic groups, the proportion of commuting pairs is always zero.
Paraules clau
Abelian Groups, Degree Of Commutativity, Polynomial Growth
Grup de recerca
MD - Matemàtica Discreta

Participants