Groups
We first state the three isomorphism theorems in the context of groups. Note that some sources switch the numbering of the second and third theorems. Sometimes, the lattice theorem is referred to as the fourth isomorphism theorem or the correspondence theorem.
Read more about this topic: Isomorphism Theorem
Famous quotes containing the word groups:
“Under weak government, in a wide, thinly populated country, in the struggle against the raw natural environment and with the free play of economic forces, unified social groups become the transmitters of culture.”
—Johan Huizinga (1872–1945)
“Writers and politicians are natural rivals. Both groups try to make the world in their own images; they fight for the same territory.”
—Salman Rushdie (b. 1947)
“As in political revolutions, so in paradigm choice—there is no standard higher than the assent of the relevant community. To discover how scientific revolutions are effected, we shall therefore have to examine not only the impact of nature and of logic, but also the techniques of persuasive argumentation effective within the quite special groups that constitute the community of scientists.”
—Thomas S. Kuhn (b. 1922)