Abstract:
In this talk we will discuss lower bounds for minimal exponential
growth rate $\Omega(G*H)$ of the free product of groups $G$ and $H$.
A.Mann has proved that $\Omega(G*H)\geqslant \sqrt{2}$ for all free
products $G*H$ except when it is a free product $C_2*C_2$ of two
cyclic groups of order $2$. This lower bound is precise in the case of
$C_2*C_3$, i.e. $\Omega(C_2*C_3)=\sqrt{2}$.
We prove that in the cases when $G*H$ is neither $C_2*C_2$ nor
$C_2*C_3$, the lower bound of A.Mann can be strengthened, namely
$\Omega(G*H)\geqslant \frac{1+\sqrt{5}}2$. This talk is based on a
joint work with M.Bucher-Karlsson.
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