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Growth of positive words and lower bounds of the growth rate for Thompson’s groups F(p)

Autor
Burillo, J.; Guba, V.
Tipus d'activitat
Article en revista
Revista
International journal of algebra and computation
Data de publicació
2017-01-20
Volum
27
Número
1
Pàgina inicial
1
Pàgina final
21
DOI
https://doi.org/10.1142/S0218196717500011 Obrir en finestra nova
URL
http://www.worldscientific.com/doi/abs/10.1142/S0218196717500011 Obrir en finestra nova
Resum
Let F(p), p=2 be the family of generalized Thompson’s groups. Here, F(2) is the famous Richard Thompson’s group usually denoted by F. We find the growth rate of the monoid of positive words in F(p) and show that it does not exceed p+1/2. Also, we describe new normal forms for elements of F(p) and, using these forms, we find a lower bound for the growth rate of F(p) in its natural generators. This lower bound asymptotically equals (p-1/2)log2e+1/2 for large values of p.
Paraules clau
Generalized Thompson’s groups, growth
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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