%0 Journal Article %T Groups with reality and conjugacy conditions %A David Chillag %A Patrizia Longobardi %A Mercede Maj %J International Journal of Group Theory %D 2012 %I University of Isfahan %X 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. %K Conjugacy classes %K real elements %K FC-groups %U http://www.theoryofgroups.ir/?_action=showPDF&article=715&_ob=6f754fe72c9779f6e33f857d2399a1c3&fileName=full_text.pdf