The relative hyperbolicity of one-relator relative presentations
نویسندگان
چکیده
منابع مشابه
The Structure of One-relator Relative Presentations and Their Centres
Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G∪{x 1 , . . . , x ±1 n } such that the word w ′ ∈ F (x1, . . . , xn) obtained from w by erasing all letters belonging to G is not a proper power in the free group F (x1, . . . , xn). We show how to reduce the study of the relative presentation Ĝ = 〈G, x1, x2, . . . , xn w = 1〉 to the case n = 1. It turns out that...
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Note that the existence of free subgroups in G̃ for n > 3 follows immediately from the free subgroup theorem for one-relator groups. Thus, Theorem 1 is nontrivial only for n = 2. The most difficult case is n = 1. An important role in this situation is played by the exponent sum of the generator in the relator. A word w = ∏ git εi ∈ G ∗ 〈t〉∞ is called unimodular if ∑ εi = 1. If the exponent sum o...
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Adding two generators and one arbitrary relator to a nontrivial torsion-free group, we always obtain an SQ-universal group. In the course of the proof of this theorem, we obtain some other results of independent interest. For instance, adding one generator and one relator in which the exponent sum of the additional generator is one to a free product of two nontrivial torsion-free groups, we als...
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Let G = a 1 ,. .. , a n | a i a j a i · · · = a j a i a j. .. , i < j be an Artin group and let m ij = m ji be the length of each of the sides of the defining relation involving a i and a j. We show if all m ij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups a i , a j for which m ij < ∞.
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2009
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2009.025