The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan

RAIRO - Theoretical Informatics and 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 45.3 (2011): 301-309. <http://eudml.org/doc/221971>.

@article{Pahlevanyan2011,
abstract = { We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd $n\geq 665$ and even $n = 16k \geq 8000$. },
author = {Pahlevanyan, Ashot S.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Free periodic groups; Burnside groups; group automorphisms; Fibonacci morphism; Fibonacci sequence; Fibonacci word; golden ratio},
language = {eng},
month = {9},
number = {3},
pages = {301-309},
publisher = {EDP Sciences},
title = {The Fibonacci automorphism of free Burnside groups},
url = {http://eudml.org/doc/221971},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Pahlevanyan, Ashot S.
TI - The Fibonacci automorphism of free Burnside groups
JO - RAIRO - Theoretical Informatics and Applications
DA - 2011/9//
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 $n\geq 665$ and even $n = 16k \geq 8000$.
LA - eng
KW - Free periodic groups; Burnside groups; group automorphisms; Fibonacci morphism; Fibonacci sequence; Fibonacci word; golden ratio
UR - http://eudml.org/doc/221971
ER -

References

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

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