Configuration sets; a right place for ping-pong arguments
Publish Year: 1403
نوع سند: مقاله ژورنالی
زبان: English
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JR_JDMA-9-3_004
تاریخ نمایه سازی: 15 شهریور 1403
Abstract:
Giving a condition for the amenability of groups, Rosenblatt and Willis first introducedthe 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.
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Authors
Meisam Soleimani Malekan
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University