The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2011)

  • Volume: 45, Issue: 3, page 301-309
  • ISSN: 0988-3754

Abstract

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We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd n ≥ 665 and even n = 16 k ≥ 8000 .

How to cite

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Pahlevanyan, Ashot S.. "The Fibonacci automorphism of free Burnside groups." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 45.3 (2011): 301-309. <http://eudml.org/doc/273005>.

@article{Pahlevanyan2011,
abstract = {We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd $n\ge 665$ and even $n = 16k \ge 8000$.},
author = {Pahlevanyan, Ashot S.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {free periodic groups; Burnside groups; group automorphisms; Fibonacci morphism; Fibonacci sequence; Fibonacci word; golden ratio; free Burnside groups; automorphisms; Fibonacci words},
language = {eng},
number = {3},
pages = {301-309},
publisher = {EDP-Sciences},
title = {The Fibonacci automorphism of free Burnside groups},
url = {http://eudml.org/doc/273005},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Pahlevanyan, Ashot S.
TI - The Fibonacci automorphism of free Burnside groups
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 3
SP - 301
EP - 309
AB - We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd $n\ge 665$ and even $n = 16k \ge 8000$.
LA - eng
KW - free periodic groups; Burnside groups; group automorphisms; Fibonacci morphism; Fibonacci sequence; Fibonacci word; golden ratio; free Burnside groups; automorphisms; Fibonacci words
UR - http://eudml.org/doc/273005
ER -

References

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  1. [1] S.I. Adian, The Burnside Problem and Identities in Groups. Nauka (1975); English translation, Springer-Verlag (1979) 1–336. Zbl0306.20045MR537580
  2. [2] V.S. Atabekyan, Non- ϕ -admissible normal subgroups of free Burnside groups. J. Contemp. Math. Anal.45 (2010) 112–122. Zbl1299.20046MR2668046
  3. [3] V.S. Atabekyan, Normal automorphisms of free Burnside groups. Izv. RAN. Ser. Math.75 (2011) 3–18. Zbl1227.20030MR2830240
  4. [4] E.A. Cherepanov, Free semigroup in the group of automorphisms of the free Burnside group. Comm. Algebra33 (2005) 539–547. Zbl1121.20028MR2124343
  5. [5] E.A. Cherepanov, Normal automorphisms of free Burnside groups of large odd exponents. Int. J. Algebra Comput.16 (2006) 839–847. Zbl1115.20024MR2274717
  6. [6] J. Karhumäki, On cube-free ω -words generated by binary morphisms. Disc. Appl. Math.5 (1983) 279–297. Zbl0505.03022MR690339
  7. [7] Kourovka Notebook, Unsolved Problems in Group Theory. Novosibirsk (2006). Zbl1084.20001MR1733915
  8. [8] I.G. Lysënok, Infinite Burnside groups of even exponent. Izv. Math.60 (1996) 453–654. Zbl0926.20023MR1405529
  9. [9] F. Mignosi and G. Pirillo, Repetitions in the Fibonacci infinite word. Informatique Théorique et Applications26 (1992) 199–204. Zbl0761.68078MR1170322

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