In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive integer n. Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups.
Read more about Divisible Group: Definition, Examples, Properties, Structure Theorem of Divisible Groups, Injective Envelope, Reduced Abelian Groups, Generalization
Famous quotes containing the words divisible and/or group:
“Knowledge, like matter, [my father] would affirm, was divisible in infinitum;Mthat the grains and scruples were as much a part of it, as the gravitation of the whole world.—In a word, he would say, error was error,—no matter where it fell,—whether in a fraction,—or a pound,—’twas alike fatal to truth.”
—Laurence Sterne (1713–1768)
“The boys think they can all be athletes, and the girls think they can all be singers. That’s the way to fame and success. ...as a group blacks must give up their illusions.”
—Kristin Hunter (b. 1931)