New York Journal of Mathematics
Volume 23 (2017) 1427-1445


Ali Rejali and Meisam Soleimani Malekan

Solubility of groups can be characterized by configuration

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Published: October 14, 2017
Keywords: Configuration, amenability, commutator subgroup, FC-group, soluble group, finitely presented group, Hopfian group
Subject: 20F05, 20F16, 20F24, 43A07

The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we investigate a condition on configuration pairs, which leads to isomorphism. We introduce a somewhat different notion of configuration equivalence, namely strong configuration equivalence, and prove that strong configuration equivalence coincides with isomorphism.

Author information

Ali Rejali:
Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan, 81746-73441, Iran

Meisam Soleimani Malekan:
Department of Mathematics, Ph.D. student, University of Isfahan, Isfahan, Iran