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
  1. Scott (1987), 15.1.1, p. 441.
  2. 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. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.