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

الأصل · EN

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)₂ e+1/2 for large values of p.