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.
Notes
Scott (1987), 15.1.1, p. 441.
Scott (1987), 15.1.2, p. 441.
References
Scott, W. R. (1987), "15.1 FC groups", Group Theory, Dover, pp. 441–446. Reprint of Prentice-Hall edition, 1964.
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