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:
“Caprice, independence and rebellion, which are opposed to the social order, are essential to the good health of an ethnic group. We shall measure the good health of this group by the number of its delinquents. Nothing is more immobilizing than the spirit of deference.”
—Jean Dubuffet (1901–1985)
“Lucretius
Sings his great theory of natural origins and of wise conduct; Plato
smiling carves dreams, bright cells
Of incorruptible wax to hive the Greek honey.”
—Robinson Jeffers (1887–1962)
“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)