Group properties characterised by configurations
Abdollahi, Alireza ; Rejali, Ali ; Willis, George A.
Illinois J. Math., Tome 48 (2004) no. 3, p. 861-873 / Harvested from Project Euclid
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J. M. Rosenblatt and G. A. Willis introduced the notion of configurations for finitely generated groups $G$. They characterised amenability of $G$ in terms of the configuration equations. In this paper we investigate which group properties can be characterised by configurations. It is proved that if $G_1$ and $G_2$ are two finitely generated groups having the same configuration sets and $G_1$ satisfies a semigroup law, then $G_2$ satisfies the same semigroup law. Furthermore, if $G_1$ is abelian then $G_1$ and $G_2$ are isomorphic.
Publié le : 2004-07-15
Classification:  43A07,  20F99 
@article{1258131056,
     author = {Abdollahi, Alireza and Rejali, Ali and Willis, George A.},
     title = {Group properties characterised by configurations},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 861-873},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258131056}
}

Abdollahi, Alireza; Rejali, Ali; Willis, George A. Group properties characterised by configurations. Illinois J. Math., Tome 48 (2004) no. 3, pp.  861-873. http://gdmltest.u-ga.fr/item/1258131056/