On the hyperbolicity of small cancellation groups and one-relator groups
نویسندگان
چکیده
منابع مشابه
On the Hyperbolicity of Small Cancellation Groups and One-relator Groups
In the article, a result relating to maps (= finite planar connected and simply connected 2-complexes) that satisfy a C(p)&T (q) condition (where (p, q) is one of (3, 6), (4, 4), (6, 3) which correspond to regular tessellations of the plane by triangles, squares, hexagons, respectively) is proven. On the base of this result a criterion for the Gromov hyperbolicity of finitely presented small ca...
متن کاملOn One-relator Inverse Monoids and One-relator Groups
It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
متن کاملAutomorphisms of One-relator Groups
It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...
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If S is noncompact, or has nonempty boundary, then π1(S) is free, and the answer to Question 1 is yes, by an old result of Magnus [7] on one-relator groups. (Essentially, the defining relator in a one-relator group on a given generating set is unique up to conjugacy and inversion.) We will show (see Theorem 3.4 below) that Question 1 also has an affirmative answer in the case of a closed surfac...
متن کاملDelzant’s T-invariant and One-relator Groups
We prove that for " most " one-relator groups Delzant's T-invariant (which measures the smallest size of a finite presentation for a group) is comparable in magnitude with the length of the defining relator. The proof relies on our previous results regarding algebraic rigidity of generic one-relator groups and on the methods of algorithmic probability involving Kolmogorov-Chaitin complexity.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1998
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-98-01818-2