1,484 research outputs found
Construction of defining relators for finite groups
AbstractGiven a faithful representation of a group G of order up to 104, we describe an algorithm, based on the notion of the graph of G, for constructing a concise presentation for G. This technique may be generalized to give a semialgorithm which is usually successful in finding presentations for groups of order up to 106
Minimal Seifert manifolds for higher ribbon knots
We show that a group presented by a labelled oriented tree presentation in
which the tree has diameter at most three is an HNN extension of a finitely
presented group. From results of Silver, it then follows that the corresponding
higher dimensional ribbon knots admit minimal Seifert manifolds.Comment: 33 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTMon1/paper12.abs.htm
Graphical small cancellation groups with the Haagerup property
We prove the Haagerup property (= Gromov's a-T-menability) for finitely
generated groups defined by infinite presentations satisfying the graphical
C'(lambda)-small cancellation condition with respect to graphs endowed with a
compatible wall structure. We deduce that these groups are coarsely embeddable
into a Hilbert space and that the strong Baum-Connes conjecture and, hence, the
Baum-Connes conjecture with arbitrary coefficients hold for them. As the main
step we show that C'(lambda)-complexes satisfy the linear separation property.
Our result provides many new examples and a general technique to show the
Haagerup property for graphical small cancellation groups.Comment: 29 pages, minor modifications to v
Pure braid subgroups of braided Thompson's groups
We describe pure braided versions of Thompson's group F. These groups,
and , are subgroups of the braided versions of Thompson's group V,
introduced by Brin and Dehornoy. Unlike V, elements of F are order-preserving
self-maps of the interval and we use pure braids together with elements of F
thus preserving order. We define these groups and give normal forms for
elements and describe infinite and finite presentations of these groups.Comment: 26 pages, 6 figures, with updated bibliograph
Rips construction without unique product
Given a finitely presented group we produce a short exact sequence such that is a torsion-free
Gromov hyperbolic group without the unique product property and is without
the unique product property and has Kazhdan's Property (T). Varying we
show a wide diversity of concrete examples of Gromov hyperbolic groups without
the unique product property. As an application, we obtain Tarski monster groups
without the unique product property.Comment: 22 page
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