Groups with small centralizers of noncentral elements

The authors classify finite groups in which the order of each centralizer of a noncentral element has at most two prime factors. There are several types of such solvable groups and the nonsolvable ones are SL(2,5) and PSL(2,5) . The result is an analogue of similar results that were proved recently for groups with arithmetical conditions on the sizes of the conjugacy classes of the noncentral elements.