# References¶

The main reference is to the paper describing theory behind these algorithms.

[BDR] | N. Barker, A. J. Duncan, and D. M. Robertson, “The power conjugacy problem in Higman-Thompson groups”, International Journal of Algebra and Computation 26, Issue 2 (2016). Preprint available at arXiv:1503.01032 [math.GR]. |

## From the paper¶

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[BBG11] | C. Bleak, H. Bowman, A. Gordon, G. Graham, J. Hughes, F. Matucci and J. Sapir, “Centralizers in R.Thompson’s group \(V_{n}\)“, Groups, Geometry and Dynamics 7 , No. 4 (2013), 821–865. |

[BCR] | J. Burillo, S. Cleary and C. E. R”over, “Obstructions for subgroups of Thompson’s group \(V\)“, arxiv.org/abs/1402.3860 |

[BK08] | V. N. Bezverkhnii, A.N. Kuznetsova, “Solvability of the power conjugacy problem for words in Artin groups of extra large type”, Chebyshevskii Sb. 9 (1) (2008) 50–68. |

[BM07] | J. M. Belk and F. Matucci, “Conjugacy and dynamics in Thompson’s groups”, Geom. Dedicata 169 (1) (2014) 239–261. |

[BMOV] | O. Bogopolski, A. Martino, O. Maslakova and E. Ventura, “The conjugacy problem is solvable in free-by-cyclic groups”, Bulletin of the London Mathematical Society , 38 , (10) (2006) 787–794. |

[Bar] | N. Barker, “Topics in Algebra: The Higman-Thompson Group \(G_{2,1}\) and Beauville \(p\)-groups”, Thesis, Newcastle University (2014) |

[Bez14] | N. V. Bezverhnii, “Ring Diagrams with Periodic Labels and Power Conjugacy Problem in Groups with Small Cancellation Conditions C (3) -T (6)”, Science and Education of the Bauman MSTU , 14 (11) (2014). |

[Brin04] | M. G. Brin, “Higher dimensional Thompson groups”, Geom. Dedicata , 108 (2004) 163–192. |

[CFP96] | J. W. Cannon, W.J. Floyd and W. R. Parry, “Introductory notes on Richard Thompson’s groups”, Enseign. Math. , (2) 42 (3–4) (1996) 215–256. |

[Cohn81] | P. M. Cohn, “Universal Algebra”. Mathematics and its Applications, 6, D. Reidel Pub. Company, (1981). |

[Cohn91] | P. M. Cohn, “Algebra, Volume 3”. J. Wiley, (1991). |

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[DMP14] | W. Dicks, C. Martinez-Pérez, “Isomorphisms of Brin-Higman-Thompson groups”, Israel Journal of Mathematics , 199 (2014), 189–218. |

[Fes14] | A. V. Fesenko, “Vulnerability of Cryptographic Primitives Based on the Power Conjugacy Search Problem in Quantum Computing”, Cybernetics and Systems Analysis , 50 (5) (2014) 815–816. |

[Hig74] | G. Higman, “Finitely presented infinite simple groups”, Notes on Pure Mathematics , Vol. 8 (1974). |

[JT61] | B. Jónsson and A. Tarski, “On two properties of free algebras”, Math. Scand. , 9 (1961) 95–101. |

[KA09] | D. Kahrobaei and M. Anshel, “Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem”, Groups-Complexity-Cryptology , 1 (2) (2009) 217-–225. |

[LM71] | S. Lipschutz and C.F. Miller, “Groups with certain solvable and unsolvable decision problems”, Comm. Pure Appl. Math. , 24 (1971) 7–15. |

[Lot83] | M. Lothaire, “Combinatorics on Words”, Addison-Wesley, Advanced Book Program, World Science Division, (1983). |

[MPN13] | C. Martinez-Perez, B. Nucinkis, “Bredon cohomological finiteness conditions for generalisations of Thompson’s groups”, Groups Geom. Dyn. 7 (4) (2013) 931–959. |

[MT73] | R. McKenzie and R. J. Thompson, “An elementary construction of unsolvable word problems in group theory”, Word problems: decision problems and the Burnside problem in group theory, Studies in Logic and the Foundations of Math., 71, pp. 457–478. North-Holland, Amsterdam, (1973). |

[Pa11] | E. Pardo, “The isomorphism problem for Higman-Thompson groups”, Journal of Algebra , 344 (2011), 172–183. |

[Pr08] | S. J. Pride, “On the residual finiteness and other properties of (relative) one-relator groups”, Proc. Amer. Math. Soc. 136 (2) (2008) 377–386. |

[R15] | D. M. Robertson, “`thompson` : a package for Python 3.3+ to work with elements of the Higman-Thompson groups \(G_{n,r}\)“. Source code available from https://github.com/DMRobertson/thompsons_v and documentation available from http://thompsons-v.readthedocs.org/. |

[SD10] | O. P. Salazar-Diaz, “Thompson’s group V from a dynamical viewpoint”, Internat. J. Algebra Comput. , 1, 39–70, 20, (2010). |

[Tho] | R. J. Thompson, unpublished notes. http://www.math.binghamton.edu/matt/thompson/index.html |

## Other references¶

[Kogan] | R. Kogan, “nVTrees Applet” (2008). Accessed 17th September, 2014. Source code available on GitHub. |

[Scott] | E. Scott, “A finitely presented simple group with unsolvable conjugacy problem, Journal of Algebra 90, Issue 2, pp. 333–353 (1984). |

[Zaks] | S. Zaks, “Lexicographic generation of ordered trees”, Theoretical Computer Science 10: 63–82 (1980). |