Delzant's $T$-invariant, Kolmogorov complexity and one-relator groups
نویسندگان
چکیده
منابع مشابه
Delzant’s T-invariant, Kolmogorov Complexity and One-relator Groups
We prove that for " random " one-relator groups the Delzant T-invariant (which measures the smallest size of a finite presentation of a group) is comparable in magnitude with the length of the defining relator. The proof relies on our previous results regarding isomorphism rigidity of generic one-relator groups and on the methods of the theory of Kolmogorov-Chaitin complexity.
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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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...
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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...
متن کاملConjugacy Separability of Some One-Relator Groups
Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2005
ISSN: 0010-2571
DOI: 10.4171/cmh/39