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.
gollark: I have some code doing this```lualocal function fetch(url, data) local res, err = net.request(url, json.encode(data), { ["Content-Type"] = "application/json" }) if not res then error(url .. " error: " .. err) end local out = {} while true do local chunk, err = res.read() if err then error(url .. " error: " .. err) end if chunk then table.insert(out, chunk) else return table.concat(out) end endend```but it never appears to `computer.pullSignal` at all, so my accursed bare-metal multithreading thing™ doesn't work.
gollark: Is there a way to do `internet.request` (with an internet card) and anything else whatsoever concurrently?
gollark: OC2 should have hard disk firmware so people can write rootkits for it.
gollark: So GHC?
gollark: I think reactor stuff just works directly as a peripheral. Fusion reactors do anyway.

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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