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math.GR2013★ 3 cited
Non-amenability of product replacement graphs
Anton Malyshev
We prove non-amenability of the product replacement graphs Γ_n(G) for uniformly non-amenable groups. We also prove it for Z-large groups, when n is sufficiently large. It follows t…
math.GR2013★ 4 cited
Growth in product replacement graphs
Anton Malyshev, Igor Pak
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…