FC-group explained

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

• . Reprint of Prentice-Hall edition, 1964.

Notes and References

1. , 15.1.1, p. 441.
2. , 15.1.2, p. 441.