Finitely Generated Group

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 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 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 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)