Noidypoos on 2/4/2008 at 13:31

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A group G is said to be abelian, or commutative, if the operation satisfies the commutative law. That is, for all a and b in G, a * b = b * a. If not, the group is called non-abelian or non-commutative. The name "abelian" comes from the Norwegian mathematician Niels Abel. The above example of symmetries of the square is non-abelian, because

r1 · fv = f2 ≠ f1 = fv · r1.

The center of a group is a subgroup consisting of the elements which commute with every other element in the group. In a commutative group the center is the whole group; at the other extreme there are groups whose center is trivial, i.e. it consists only of the identity element.

Stitch on 2/4/2008 at 19:05

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Now that's how you do it :cool:

Aja on 3/4/2008 at 01:10

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oh for fucks sake

Noidypoos on 3/4/2008 at 07:35

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No use for it apart from the fact that it one of the most important areas of mathematics to be integrated into the science of physics in this century and the last, helping us make massive breakthroughs in the study of quantum physics and symmetry.

And I won't even mention that the powerful abstractions it creates allow us to make general statements about entire families of mathematical structures providing we identify them as certain groups

Shug on 3/4/2008 at 13:05

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if we needed the ttlg police on this one I would already have reported the post to catbarf