The quotient group G/G0 is called the group of components or component group of G. Its elements are just the connected components of G. The component group G/G0 is a discrete group if and only if G0 is open. If G is an affine algebraic group then G/G0 is actually a finite group.
One may similarly define the path component group as the group of path components (quotient of G by the identity path component), and in general the component group is a quotient of the path component group, but if G is locally path connected these groups agree. The path component group can also be characterized as the zeroth homotopy group,
Read more about this topic: Identity Component
Famous quotes containing the words component and/or group:
“... no one knows anything about a strike until he has seen it break down into its component parts of human beings.”
—Mary Heaton Vorse (1874–1966)
“...Women’s Studies can amount simply to compensatory history; too often they fail to challenge the intellectual and political structures that must be challenged if women as a group are ever to come into collective, nonexclusionary freedom.”
—Adrienne Rich (b. 1929)