University of Isfahan International Journal of Group Theory 2251-7650 1 2 2012 06 01 Groups with reality and conjugacy conditions 25 38 715 10.22108/ijgt.2012.715 EN David Chillag Patrizia Longobardi Dipartimento di Matematica Universit`a di Salerno Via Ponte don Melillo 84084 - Fisciano (SA), Italy Mercede Maj Journal Article 2011 11 18 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. https://ijgt.ui.ac.ir/article_715_6f754fe72c9779f6e33f857d2399a1c3.pdf