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Original Articles

The Lamplighter Group ℤ3≀ℤ Generated by a Bireversible Automaton

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Pages 5257-5268 | Received 24 Apr 2015, Published online: 06 Jul 2016

REFERENCES

  • Bartholdi, L., Silva, P. (2010). Groups defined by automata. Available at http://arxiv.org/abs/1012.1531.
  • Bartholdi, L., Šuniḱ, Z. (2006). Some solvable automaton groups. Contemp. Math. 394:11–29.
  • D'Angeli, D., Rodaro, E. (2014). Groups and semigroups defined by colorings of synchronizing automata. Int. J. Algebra Comput. 24(6):773–793.
  • Glasner, Y., Mozes, S. (2005). Automata and square complexes. Geometriae Dedicata 111:43–64.
  • Grigorchuk, R. I., Kravchenko, R. (2015). On the lattice of subgroups of the Lamplighter group. Int. J. Algebra Comput. 24:837–877.
  • Grigorchuk, R. I., Linnell, P., Schick, T., Żuk, A. (2000). On a question of Atiyah. C. R. Acad. Sci., Paris, Sér. I, Math. 331(9):663–668.
  • Grigorchuk, R. I., Nekrashevych, V. V., Sushchansky, V. I. (2000). Automata dynamical systems and groups. Proc. Steklov Inst. Math. 231:128–203.
  • Grigorchuk, R. I., Šuniḱ, Z. (2007). Self-similarity and branching in group theory, London Math. Soc. Lect. Note Ser. 339:36–95.
  • Grigorchuk, R. I., Żuk, A. (2001). The Lamplighter group as a group generated by a 2-state automaton, and its spectrum. Geometriae Dedicata 87(13):209–244.
  • Macedońska, O., Nekrashevych, V., Sushchansky, V. (2000). Commensurators of groups and reversible automata. Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 12:36–39.
  • Muntyan, Y., Savchuk, D. (2008). AutomGrp—GAP package for computations in self-similar groups and semigroups, Version 1.1.2.
  • Nekrashevych, V. (2005). Self-similar Groups. Mathematical Surveys and Monographs, Vol. 117, Providence: Amerimay Mathematical Society.
  • Savchuk, D., Sidki, S. (2015). Affine automorphisms of rooted trees. Preprint: arxiv:1510.08434.
  • Savchuk, D., Vorobets, Y. (2011). Automata generating free products of groups of order 2. J. Algebra 336(1):53–66.
  • Silva, P. V., Steinberg, B. (2005). On a class of automata groups generalizing lamplighter groups. Int. J. Algebra Comput. 15(5–6):1213–1234.
  • Steinberg, B., Vorobets, M., Vorobets, Y. (2011). Automata over a binary alphabet generating free groups of even rank. Int. J. Algebra Comput. 21(1–2):329–354.
  • Vorobets, M., Vorobets, Y. (2007). On a free group of transformations defined by an automaton, Geometriae Dedicata 124:237–249.
  • Vorobets, M., Vorobets, Y. (2010). On a series of finite automata defining free transformation groups. Groups Geome. Dyn. 4(2):377–405.

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