Giving a condition for the amenability of groups, Rosenblatt and Willis first introduced the concept of configuration. In this paper, we investigate the relationship between ping-pong lemma and configuration sets, and show that only one configuration set is enough to ensure that several elements in a group generates a free subgroup of that group. Using only one two-sided configuration sets, we give, in a sense, a generalization of this result to polycyclic or FC-groups. Finiteness and paradoxical decompositions of groups, are other properties which can be characterized with only one configuration set.
Soleimani Malekan, M. (2024). Configuration sets; a right place for ping-pong arguments. Journal of Discrete Mathematics and Its Applications, 9(3), 191-202. doi: 10.22061/jdma.2024.11140.1079
MLA
Meisam Soleimani Malekan. "Configuration sets; a right place for ping-pong arguments". Journal of Discrete Mathematics and Its Applications, 9, 3, 2024, 191-202. doi: 10.22061/jdma.2024.11140.1079
HARVARD
Soleimani Malekan, M. (2024). 'Configuration sets; a right place for ping-pong arguments', Journal of Discrete Mathematics and Its Applications, 9(3), pp. 191-202. doi: 10.22061/jdma.2024.11140.1079
VANCOUVER
Soleimani Malekan, M. Configuration sets; a right place for ping-pong arguments. Journal of Discrete Mathematics and Its Applications, 2024; 9(3): 191-202. doi: 10.22061/jdma.2024.11140.1079
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