Titlebook: Algorithms and Classification in Combinatorial Group Theory; Gilbert Baumslag,Charles F. Miller Book 1992 Springer-Verlag New York, Inc. 1

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sigmoid-colon

The Geometry of Rewriting Systems: A Proof of the Anick-Groves-Squier Theorem,ssifying space of . down to a quotient complex (typically “small”) of the same homotopy type. If the rewriting system is finite, then the quotient complex has only finitely many cells in each dimension. The proof yields an explicit free resolution of . over .., similar to resolutions obtained by Anick, Groves, and Squier.

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Combings of Groups, yields, via a theorem of Ken Brown, a proof that automatic groups are finitely presented and of type ... We also characterize hyperbolic groups in terms of combings, and discuss the relationship between the combings considered here and isoperimetric inequalities.

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https://doi.org/10.1007/978-1-84882-539-0mples of infinite simple groups. For example, let .. be any non-trivial torsion free group. Then, by [3], there exists a torsion free group C., containing .., in which the non-trivial elements of .. are all conjugate to each other. For . ∈ ℤ define ... = C. and let . = ∪.C.. Then . is an infinite simple group.

EXULT

The School Mathematical Education,the Cantor set. For each . ∈ . and each integer . ≥ 1, an (. −1)-connected .-dimensional simplicial complex is constructed, on which . acts with finite stabilizers and with an .-simplex as fundamental domain. This yields homological and combinatorial information about .. As a by-product, one obtains a solution to a problem of Neumann and Neumann.

refraction

The School Mathematical Education,ssifying space of . down to a quotient complex (typically “small”) of the same homotopy type. If the rewriting system is finite, then the quotient complex has only finitely many cells in each dimension. The proof yields an explicit free resolution of . over .., similar to resolutions obtained by Anick, Groves, and Squier.