Abstract In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the group. We also show that the set of centralizers that are minimal under the partial ordering form a cover of the group. We show for F -groups that are nonabelian p -groups that the number of distinct nontrivial centralizers is congruent to 1 modulo p .
Lewis et al. (Tue,) studied this question.