Group Theory Generalized
Much of group theory can be formulated in the context of the more general group objects. The notions of group homomorphism, subgroup, normal subgroup and the isomorphism theorems are typical examples. However, results of group theory that talk about individual elements, or the order of specific elements or subgroups, normally cannot be generalized to group objects in a straightforward manner.
Read more about this topic: Group Object
Famous quotes containing the words group, theory and/or generalized:
“The government of the United States at present is a foster-child of the special interests. It is not allowed to have a voice of its own. It is told at every move, “Don’t do that, You will interfere with our prosperity.” And when we ask: “where is our prosperity lodged?” a certain group of gentlemen say, “With us.””
—Woodrow Wilson (1856–1924)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)