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,
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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)
“No other group in America has so had their identity socialized out of existence as have black women.... When black people are talked about the focus tends to be on black men; and when women are talked about the focus tends to be on white women.”
—bell hooks (b. c. 1955)