group theory, Gromov's theorem on groups of polynomial growth, first proved by Mikhail Gromov, characterizes finitely generated groups of polynomial growth...

Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems: Gromov's compactness theorem (geometry) in...

contains a nilpotent subgroup of finite index). See Gromov's theorem on groups of polynomial growth. (Also see D. Edwards for an earlier work.) The key...

Gromov and others into the more flexible notion of an ultralimit.[G93] Gromov's compactness theorem had a deep impact on the field of geometric group...

nonabelian version of Freiman's theorem, and a generalization of Gromov's theorem on groups of polynomial growth. If A is a set of N integers, how large...

Gromov's theorem on groups of polynomial growth (geometric group theory) Gromov–Ruh theorem (differential geometry) Gross–Zagier theorem (number theory)...

theorem or L. van den Dries and Alex Wilkie's treatment of Gromov's theorem on groups of polynomial growth. Nonstandard analysis was used by Larry Manevitz and...

ISBN 0-8218-2129-6. MR 1835418. Zbl 0981.51016. (Erratum:  [1]) Gromov, Mikhael (1981). "Groups of polynomial growth and expanding maps". Publications Mathématiques de...

the proof of Gromov's theorem on groups of polynomial growth. In fact the alternative essentially establishes the result for linear groups (it reduces...

a polynomial growth rate. The infimum k 0 {\displaystyle k_{0}} of such k's is called the order of polynomial growth. According to Gromov's theorem, a...

polynomial function and slower than any exponential function. An important result in the subject is Gromov's theorem on groups of polynomial growth,...

(in July). Kleiner found a relatively simple proof of Gromov's theorem on groups of polynomial growth. He also proved the Cartan–Hadamard conjecture in...

Negligible set Colombeau algebra Nonstandard numbers Gromov's theorem on groups of polynomial growth Non-standard calculus Katz, Johnathan (6 November 2014)...

whole group). The Breuillard–Green–Tao theorem on classification of approximate groups can be used to give a new proof of Gromov's theorem on groups of polynomial...

Zbl 0539.13011. L. van den Dries; A. Wilkie (1984). "Gromov's theorem of groups of polynomial growth and elementary logic". J. Algebra. 89 (2): 349–374...

L.Van den Dries, A.J.Wilkie, On Gromov's theorem concerning groups of polynomial growth and elementary logic. Journal of Algebra, Vol. 89(1984), pp. 349–374...

geometric group theory, inventor of homotopy principle, introduced Gromov's compactness theorem, Gromov norm, Gromov product etc., Wolf Prize winner Leonid...

results on the structure of approximate subgroups, for example implying a strengthened version of Gromov's theorem on groups of polynomial growth. Although...

solvable groups are one of the two alternatives in the Tits alternative, while Gromov's theorem states that the finitely generated groups with polynomial growth...

others. Theorems which use quasi-isometry invariants to prove algebraic results about groups, for example: Gromov's polynomial growth theorem; Stallings'...

product of length n. According to Gromov's theorem, a group of polynomial growth is virtually nilpotent, i.e. it has a nilpotent subgroup of finite index...

Kazhdan–Lusztig polynomials at 1 with representations of complex semisimple Lie groups and Lie algebras. McKay conjecture: in a group G {\displaystyle...

fundamental group of polynomial growth. Mikhael Gromov and Blaine Lawson introduced the notion of enlargeability of a closed manifold. The class of enlargeable...

analogy with Mikhail Gromov's notion of word growth. Let G {\displaystyle G} be a finitely generated torsionfree nilpotent group. Then there exists a...

Betti numbers. Comment. Math. Helv. 56 (1981), no. 2, 179–195. Groups of polynomial growth and expanding maps. Inst. Hautes Études Sci. Publ. Math. 53 (1981)...

non-trivial fundamental group π1 = Γ; the groups that arise this way are known as Fuchsian groups. The quotient space H2‍/‍Γ of the upper half-plane modulo...

development of the theory of word-hyperbolic groups. In his 1987 monograph "Hyperbolic groups" Gromov proved that a finitely presented group is word-hyperbolic...

uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness theorems for ODE...

semisimple algebraic groups over local fields. In particular there is a wealth of rigidity results in this setting, and a celebrated theorem of Grigory Margulis...

action of a finitely-generated group with polynomial growth on a standard Borel space induces a hyperfinite orbit equivalence relation. The action of a finitely-generated...