# The Fibonacci automorphism of free Burnside groups

RAIRO - Theoretical Informatics and Applications (2011)

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

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topPahlevanyan, 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

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

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