Complete Group
In mathematics, a group G is said to be complete if every automorphism of G is inner, and the group is a centerless group; that is, it has a trivial outer automorphism group and trivial center. Equivalently, a group is complete if the conjugation map (sending an element g to conjugation by g) is an isomorphism: 1-to-1 corresponds to centerless, onto corresponds to no outer automorphisms.
Read more about Complete Group: Examples, Properties, Extensions of Complete Groups
Famous quotes containing the words complete and/or group:
“In the course of the actual attainment of selfish endsan attainment conditioned in this way by universalitythere is formed a system of complete interdependence, wherein the livelihood, happiness, and legal status of one man is interwoven with the livelihood, happiness, and rights of all. On this system, individual happiness, etc. depend, and only in this connected system are they actualized and secured.”
—Georg Wilhelm Friedrich Hegel (17701831)
“Remember that the peer group is important to young adolescents, and theres nothing wrong with that. Parents are often just as important, however. Dont give up on the idea that you can make a difference.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, I, ch.5 (1985)