On a class of groups with strongly embedded subgroup.
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.
We show that the special linear group , over the integers, is not -generated. This gives a negative answer to a question of M. Conder.