FC-group

Group in group theory mathematics

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

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1. ^ Scott (1987), 15.1.1, p. 441.
2. ^ Scott (1987), 15.1.2, p. 441.

## References

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

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