### Some articles on *finitely generated group, group, groups, finitely generated groups*:

Stallings Theorem About Ends Of Groups - Applications and Generalizations

... theorem was a proof by Stallings of a long-standing conjecture that every

... theorem was a proof by Stallings of a long-standing conjecture that every

**finitely generated group**of cohomological dimension one is free and that every torsion-free ... subgroup is a quasi-isometry invariant of a**finitely generated group**since the number of ends of a**finitely generated group**is easily seen to be a quasi-isometry invariant ... reason Stallings' theorem is considered to be one of the first results in geometric**group**theory ...Gromov's Theorem On Groups Of Polynomial Growth

... In geometric

... In geometric

**group**theory, 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 ... 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) ...Stallings Theorem About Ends Of Groups - Ends of Groups - Basic Facts and Examples

... For any

... For any

**finitely generated group**G we have e(G) ∈ {0, 1, 2, ∞} For a**finitely generated group**G we have e(G) = 0 if and only if G is finite ... For the infinite cyclic**group**we have For the free abelian**group**of rank two we have For a free**group**F(X) where 1 <### Famous quotes containing the words group and/or generated:

“A little *group* of wilful men reflecting no opinion but their own have rendered the great Government of the United States helpless and contemptible.”

—Woodrow Wilson (1856–1924)

“It is precisely the purpose of the public opinion *generated* by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.”

—Walter Benjamin (1892–1940)

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