Growth in Product Replacement Graphs
نویسنده
چکیده
We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.
منابع مشابه
Growth in Product Replacement Graphs of Grigorchuk Groups
The product replacement graph Γk(G) is the graph on the generating k-tuples of a group G, with edges corresponding to Nielsen moves. We prove the exponential growth of product replacement graphs Γk(Gω) of Grigorchuk groups, for k ≥ 5.
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تاریخ انتشار 2013