arXiv subjects
Publications and source records attributed to A. Yousofzadeh.
In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different types of well-known ping-pong lemma is also investigated.
In this paper we define countable-configuration of groups and prove that two Hopfian groups with the same set of countable-configurations are isomorphic and vice versa. We also study the countable paradoxical decomposition of groups. It is proved that a group G admits a countable paradoxical decomposition if and only if it is infinite.
The concept of configuration was first introduced by Rosenblatt and Willis to give a condition for amenability of groups. We show that if $G_1$ and $G_2$ have the same configuration sets and $H_1$ is a normal subgroup of $G_1$ with abelian quotient, then there is a normal subgroup $H_2$ of $G_2$ such that $\frac{G_1}{H_1}\cong\frac{G_2}{H_2}.$ Also configuration of FC-groups and isomorphism is studied.