On a formula for the asymptotic dimension of free products
Volume 183 / 2004
Fundamenta Mathematicae 183 (2004), 39-45
MSC: Primary 20F69; Secondary 20E08, 20E06.
DOI: 10.4064/fm183-1-2
Abstract
We prove an exact formula for the asymptotic dimension (asdim) of a free product. Our main theorem states that if $A$ and $B$ are finitely generated groups with $\mathop {\rm asdim}\nolimits A=n$ and $\mathop {\rm asdim}\nolimits B\le n$, then ${\rm asdim} (A\ast B)=\mathop {\rm max} \{n,1\}.$
