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  "body": "\n## Statement\n\nBeyond Gromov's theorem one can ask whether there exists a gap in the growth spectrum for finitely generated group just above polynomial growth, separating virtually nilpotent groups from others. Formally, this means that there would exist a function $f: \\mathbb N \\to \\mathbb N$ such that a finitely generated group is virtually nilpotent if and only if its growth function is an $O(f(n))$. Such a theorem was obtained by Shalom and Tao, with an explicit function $n^{\\log\\log(n)^c}$ for some $c \u003e 0$. All known groups with intermediate growth (i.e. both superpolynomial and subexponential) are essentially generalizations of Grigorchuk's group, and have faster growth functions; so all known groups have growth faster than $e^{n^{\\alpha-o(1)}}$, with $\\alpha = \\log(2)/\\log(2/\\eta ) \\approx 0.767$, where $\\eta$ is the real root of the polynomial $x^3+x^2+x-2$.\n\nIt is conjectured that the true lower bound on growth rates of groups with intermediate growth is $e^{\\sqrt n}$. This is known as the *Gap conjecture*.\n",
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