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On a formula for the asymptotic dimension of free products

G. C. Bell, A. N. Dranishnikov, J. E. Keesling (2004)

Fundamenta Mathematicae

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 asdim A = n and asdim B ≤ n, then asdim (A*B) = max n,1.

On a question of M. Conder

M. Chiara Tamburini, Paola Zucca (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that the special linear group S L 3 , Z , over the integers, is not 2 , 3 -generated. This gives a negative answer to a question of M. Conder.

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