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

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

2005-11-18

arxiv.org/abs/math/0511474v1

Mathematics

Group Theory

17 pages

Scientific paper

Let $F(p)$, $p\ge2$ 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 $(p-1/2)\log_2 e+1/2$ for large values of $p$.

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