Small cancellation groups and translation numbers
نویسندگان
چکیده
منابع مشابه
The Burnside Groups and Small Cancellation Theory
In a pair of recent articles, the author develops a general version of small cancellation theory applicable in higher dimensions ([5]), and then applies this theory to the Burnside groups of sufficiently large exponent ([6]). More specifically, these articles prove that the free Burnside groups of exponent n ≥ 1260 are infinite groups which have a decidable word problem. The structure of the fi...
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Let G be a group given by the presentation 〈a1, . . . , ak , b1, . . . bk | ai = ui(b̄), bi = vi(ā) for 1 ≤ i ≤ k〉, where k ≥ 2 and where the ui ∈ F (b1, . . . , bk) and wi ∈ F (a1, . . . , ak) are random words. Generically such a group is a small cancellation group and it is clear that (a1, . . . , ak) and (b1, . . . , bk) are generating n-tuples for G. We prove for generic choices of u1, . . ....
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with the property that for any pair r, s of elements of R either r = s or there is very little free cancellation in forming the product rs. The classical example of such a group is the fundamental group of a closed orientable 2-manifold of genus k. The study of this group has given rise both to the theory of one-relator groups, initiated by Magnus ([3]), and to the theory of small cancellation ...
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We work in the density model of random groups. We prove that they satisfy an isoperimetric inequality with sharp constant 1− 2d depending upon the density parameter d. This implies in particular a property generalizing the ordinary C ′ small cancellation condition, which could be termed “macroscopic cancellation”. This also sharpens the evaluation of the hyperbolicity constant δ. As a consequen...
متن کاملUnsolvable problems about small cancellation and word hyperbolic groups
We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable. Given any integer k > 2, there is no algorithm to determine whether or not any small cancellation group can be generated by either two elements or more than k elements. There is a small cancellation gro...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01653-x