We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
@article{ITA_2011__45_3_301_0, author = {Pahlevanyan, Ashot S.}, title = {The Fibonacci automorphism of free Burnside groups}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {45}, year = {2011}, pages = {301-309}, doi = {10.1051/ita/2011118}, mrnumber = {2836491}, zbl = {1227.20038}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2011__45_3_301_0} }
Pahlevanyan, Ashot S. The Fibonacci automorphism of free Burnside groups. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) pp. 301-309. doi : 10.1051/ita/2011118. http://gdmltest.u-ga.fr/item/ITA_2011__45_3_301_0/
[1] The Burnside Problem and Identities in Groups. Nauka (1975); English translation, Springer-Verlag (1979) 1-336. | MR 537580 | Zbl 0306.20045
,[2] Non--admissible normal subgroups of free Burnside groups. J. Contemp. Math. Anal. 45 (2010) 112-122. | MR 2668046 | Zbl 1299.20046
,[3] Normal automorphisms of free Burnside groups. Izv. RAN. Ser. Math. 75 (2011) 3-18. | MR 2830240 | Zbl 1227.20030
,[4] Free semigroup in the group of automorphisms of the free Burnside group. Comm. Algebra 33 (2005) 539-547. | MR 2124343 | Zbl 1121.20028
,[5] Normal automorphisms of free Burnside groups of large odd exponents. Int. J. Algebra Comput. 16 (2006) 839-847. | MR 2274717 | Zbl 1115.20024
,[6] On cube-free -words generated by binary morphisms. Disc. Appl. Math. 5 (1983) 279-297. | MR 690339 | Zbl 0505.03022
,[7] Kourovka Notebook, Unsolved Problems in Group Theory. Novosibirsk (2006). | MR 1733915
[8] Infinite Burnside groups of even exponent. Izv. Math. 60 (1996) 453-654. | MR 1405529 | Zbl 0926.20023
,[9] Repetitions in the Fibonacci infinite word. Informatique Théorique et Applications 26 (1992) 199-204. | Numdam | MR 1170322 | Zbl 0761.68078
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