Dual To Center
The outer automorphism group is dual to the center in the following sense: conjugation by an element of G is an automorphism, yielding a map The kernel of the conjugation map is the center, while the cokernel is the outer automorphism group (and the image is the inner automorphism group). This can be summarized by the short exact sequence:
Read more about this topic: Outer Automorphism Group
Famous quotes containing the words dual and/or center:
“Thee for my recitative,
Thee in the driving storm even as now, the snow, the winter-day
declining,
Thee in thy panoply, thy measur’d dual throbbing and thy beat
convulsive,
Thy black cylindric body, golden brass and silvery steel,”
—Walt Whitman (1819–1892)
“There is nothing more natural than to consider everything as starting from oneself, chosen as the center of the world; one finds oneself thus capable of condemning the world without even wanting to hear its deceitful chatter.”
—Guy Debord (b. 1931)