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Configuration sets; a right place for ping-pong arguments | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 4، دوره 9، شماره 3، آذر 2024، صفحه 191-202 اصل مقاله (309.34 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11140.1079 | ||
| نویسنده | ||
| Meisam Soleimani Malekan* | ||
| Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University | ||
| تاریخ دریافت: 16 مرداد 1403، تاریخ بازنگری: 07 شهریور 1403، تاریخ پذیرش: 09 شهریور 1403 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Configuration؛ FC-Group؛ Finitely Presented Group؛ Polycyclic Group | ||
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آمار تعداد مشاهده مقاله: 38 تعداد دریافت فایل اصل مقاله: 63 |
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