A group G is said to be sharply n-transitive if it acts on a set X (of cardinality at least n) in such a way that, for every n-tuples (x_1,...,x_n) and (y_1,..,y_n) of distinct elements of X, there exists a unique element g in G sending (x_1,...,x_n) to (y_1,..,y_n). For instance, the affine group on a field K is sharply 2-transitive (for its action on K), and PGL_2(K) is sharply 3-transitive (for its action on the projective line). I will explain that SL_3(Z) and SL_4(Z) contain, respectively, infinite (non-split) sharply 2-transitive and sharply 3-transitive groups, which answers a question of Glasner and Gulko. This is joint work with Marco Amelio, building on results of Tent and Tent-Ziegler.