Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

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Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations

- 01 Jan 1966

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About: The article was published on 01 Jan 1966. and is currently open access. The article focuses on the topics: Combinatorial group theory.

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Citations

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Growth tightness of surface groups

Andrea Sambusetti

- 01 Jan 2002

- Expositiones Mathematicae

TL;DR: In this paper, it was shown that fundamental groups of closed oriented surfaces ∑g of genus g ≥ 2 are growth tight with respect to hyperbolic metrics and to the word metric relative to their canonical presentation.

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Certain Subgroups of Certain One-Relator Groups.

Stephen J. Pride

- 01 Feb 1976

- Mathematische Zeitschrift

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- 26 Oct 2020

- arXiv: Group Theory

TL;DR: In this article, three new Coxeter groups type $A, $B, and $D$ using prefix reversals (pancake flips) as generators are presented. And they prove these presentations are of their respective groups by using Tietze transformations on the presentations to recover the well known presentations with generators that are adjacent transpositions.

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The Borsuk-Ulam property for homotopy classes of selfmaps of surfaces of Euler characteristic zero

Daciberg Lima Gonçalves, +2 more

- 01 Aug 2016

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TL;DR: In this paper, the Borsuk-Ulam property of topological spaces was studied in terms of the pure and full 2-string braid groups of N and the fundamental groups of M and the orbit space of M with respect to the action of a free involution.

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•Journal Article•10.1093/IMRN/RNT344

Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations

Andrey Minchenko, +3 more

- 09 Apr 2013

- arXiv: Representation Theory

TL;DR: In this paper, the representation theory for reductive linear differential algebraic groups (LDAGs) was developed and an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs was established.

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