For n≥6 the Kim-Manturov group Γ^4_n is finite, 2-step nilpotent, and has order 2^{binom(n,3)}.
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On the structure of groups defined by Kim and Manturov
For n≥6 the Kim-Manturov group Γ^4_n is finite, 2-step nilpotent, and has order 2^{binom(n,3)}.