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 spaceshow could explanations be possible at all when we initially turn everything into images, into our images!”
—Friedrich Nietzsche (18441900)
“Once it was a boat, quite wooden
and with no business, no salt water under it
and in need of some paint. It was no more
than a group of boards. But you hoisted her, rigged her.
Shes been elected.”
—Anne Sexton (19281974)