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

[AS74]

M. Anshel and P. Stebe, “The solvability of the conjugacy problem for certain HNN groups”, Bull. Amer. Math. Soc. , 80 (2) (1974) 266–270.

[B87]

K. S. Brown, “Finiteness properties of groups”, Journal of Pure and Applied Algebra, 44 (1987) 45-75.

[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).

[Com77]

L. P. J. Comerford, A note on power-conjugacy, Houston J. Math. 3 (1977), no. 3, 337—341.

[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).