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:
“We operate exclusively with things that do not exist, with lines, surfaces, bodies, atoms, divisible time spans, divisible spaces—how could explanations be possible at all when we initially turn everything into images, into our images!”
—Friedrich Nietzsche (1844–1900)
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—Diana Crane (b. 1933)