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.1
- Every abelian group is an FC-group.2
- The following property is stronger than the property of being FC: every subgroup has finite index in its normal closure.
References
References
- Scott, W. R. (1987), "15.1 FC groups", Group Theory, Dover, pp. 441–446. Reprint of Prentice-Hall edition, 1964.