Geodesic
On a formula for the asymptotic dimension of free products
G. C. Bell 1   ; A. N. Dranishnikov 2   ; J. E. Keesling 3
1 Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A.
2 Department of Mathematics University of Florida 358 Little Hall P.O. Box 118105 Gainesville, FL 32611-8105, U.S.A.
3 Department of Mathematics University of Florida 358 Little Hall P.O.Box 118105 Gainesville, FL, 32611-8105, U.S.A.
Fundamenta Mathematicae, Tome 183 (2004) no. 1, pp. 39-45 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 ${\rm asdim} (A\ast B)=\mathop {\rm max} \{n,1\}.$
DOI : 10.4064/fm183-1-2
Keywords: prove exact formula asymptotic dimension asdim product main theorem states finitely generated groups mathop asdim nolimits mathop asdim nolimits asdim ast mathop max

G. C. Bell  1   ; A. N. Dranishnikov  2   ; J. E. Keesling  3

1 Department of Mathematics The Pennsylvania State University University Park, PA 16802, U.S.A.
2 Department of Mathematics University of Florida 358 Little Hall P.O. Box 118105 Gainesville, FL 32611-8105, U.S.A.
3 Department of Mathematics University of Florida 358 Little Hall P.O.Box 118105 Gainesville, FL, 32611-8105, U.S.A. 
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G. C. Bell; A. N. Dranishnikov; J. E. Keesling. On a formula for the
 asymptotic dimension of free products. Fundamenta Mathematicae, Tome 183 (2004) no. 1, pp. 39-45. doi: 10.4064/fm183-1-2

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