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Preprint Number 1283
1283. Arman Darbinyan Word and conjugacy problems in lacunary hyperbolic groups E-mail: Submission date: 15 August 2017 Abstract: We study word and conjugacy problems in lacunary hyperbolic groups (briefly,
LHG). In particular, we describe a necessary and sufficient condition for
decidability of the word problem in LHG. Then, based on the graded
small-cancellation theory of Olshanskii, we develop a general framework which
allows us to construct lacunary hyperbolic groups with word and conjugacy
problems highly controllable and flexible both in terms of computability and
computational complexity. Mathematics Subject Classification: Keywords and phrases: |

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