FC-group
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.
This article is issued from Wikipedia - version of the Tuesday, January 24, 2012. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.