Journal ArticleDOI
On Torsion-Free Groups with Infinitely Many Ends
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This article is published in Annals of Mathematics.The article was published on 1968-09-01. It has received 508 citations till now. The article focuses on the topics: Torsion (algebra).read more
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The geometry and topology of Coxeter groups
TL;DR: The authors introduced the theory of Coxeter groups in the context of the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua University on May 10, 2013.
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Degrees of Growth of Finitely Generated Groups, and the Theory of Invariant Means
TL;DR: In this article, a negative solution to the problem of Milnor concerning the degrees of growth of groups was given, which also answers a question of Day concerning amenable groups and a number of other results are obtained on residually finite finitely generated infinite 2-groups.
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On Dehn's Lemma and the Asphericity of Knots
TL;DR: Dehn's lemma holds for all orientable 3-manifolds as mentioned in this paper, with the exception of non-contractible 2-spheres, which do not have a commutator quotient group.
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On the Lusternik-Schnirelmann Category of Abstract Groups
Samuel Eilenberg,T. Ganea +1 more
TL;DR: Theorem 1.1 Theorem 2.1 as mentioned in this paper Theorem 3.2 Theorem 4.3 Theorem 5.1: For any group H, the least integer n such that X can be covered by open sets UO, * * *, Un such that each Ui is contractible in X, if no such integer exists then cat X = oo.