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On the Universal Theory of Torsion and Lacunary Hyperbolic Groups
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D. Osin
Published/Copyright:
March 10, 2010
We show that the universal theory of torsion groups is strongly contained in the universal theory of finite groups. This answers a question of Dyson. We also prove that the universal theory of some natural classes of torsion groups is undecidable. Finally we observe that the universal theory of the class of hyperbolic groups is undecidable and use this observation to construct a lacunary hyperbolic group with undecidable universal theory. Surprisingly, torsion groups play an important role in the proof of the latter results.
Received: 2009-03-21
Published Online: 2010-03-10
Published in Print: 2009-October
© Heldermann Verlag
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Articles in the same Issue
- The Word and Conjugacy Problem for Shuffle Groups
- Torsion-free Abelian Factor Groups of the Baumslag-Solitar Groups and Subgroups of the Additive Group of the Rational Numbers
- Metabelian Product of a Free Nilpotent Group with a Free Abelian Group
- Almost Locally Free Groups and a Theorem of Magnus: Some Questions
- Authentication from Matrix Conjugation
- The Tits Alternative for Tsaranov's Generalized Tetrahedron Groups
- Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem
- A Note on the Shifted Conjugacy Problem in Braid Groups
- Algebraic Attacks Galore!
- Space Complexity and Word Problems of Groups
- A Practical Attack on a Certain Braid Group Based Shifted Conjugacy Authentication Protocol
- Existence and Non-Existence of Torsion in Maximal Arithmetic Fuchsian Groups
- Power-Commutative Nilpotent R-Powered Groups
- On the Universal Theory of Torsion and Lacunary Hyperbolic Groups
