In mathematics, in the field of group theory, an FC-group is a group in which every conjugacy class of elements has finite cardinality. The following are some facts about FC-groups: Every finite group is an FC-group. Every abelian group is an FC-group. The following property is stronger than the property of being FC: every subgroup has finite index in its normal closure. Notes References . Reprint of Prentice-Hall edition, 1964. Infinite group theory Properties of groups