GROUPS WITH REALITY AND CONJUGACY CONDITIONS

Abstract. Many results were proved on the structure of finite groups with some restrictions on their real elements and on their conjugacy classes. We generalize a few of these to some classes of infinite groups. We study groups in which real elements are central, groups in which real elements are 2- elements, groups in which all non-trivial classes have the same finite size and FC-groups with two non-trivial conjugacy class sizes.