Gromov's Theorem on Groups of Polynomial Growth
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Gromov''s theorem on groups of polynomial growth, named for Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which have nilpotent subgroups of finite index. The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length (relative to a symmetric generating set) at most n is bounded above by a…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Gromov''s theorem on groups of polynomial growth, named for Mikhail Gromov, characterizes finitely generated groups of polynomial growth, as those groups which have nilpotent subgroups of finite index. The growth rate of a group is a well-defined notion from asymptotic analysis. To say that a finitely generated group has polynomial growth means the number of elements of length (relative to a symmetric generating set) at most n is bounded above by a polynomial function p(n). The order of growth is then the least degree of any such polynomial function p.