abelian
- adjective
- /əˈbiːliən/
- Specialized
:
abeliano
- If you know what a group is, you will observe that addition modulo n is an abelian group, with the congruence classes as elements.
- abelian gauge
- abelian case
But are there genuinely new examples of sets in non abelian groups that have bounded doubling?
- But are there genuinely new examples of sets in non abelian groups that have bounded doubling?
- OK, They become Yang Miel theory and somehow they become non abelian, OK.
Examples
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When studying algebra, you'll find that any two elements in an abelian structure can be combined without affecting the outcome.
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So suppose H is abelian, and the claim this time is that G is.
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So G is abelian and that completes the proof.
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More interestingly, multiplication on the classes coprime to n is also an abelian group, though its properties are less obvious.
Blog text (31) -
In QED, the gauge transformations are Abelian—that is, commutative; the order of two transformations in succession doesn't matter.
Academic text (1999) -
In an abelian group, the sum of two elements is the same regardless of their order.
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The integers under addition form an abelian group, meaning a + b = b + a for any integers a and b.
Synonyms
1
7.9
An operation where changing the order of numbers does not change the result
Compounds
Surface Forms
Etymology
Abelian is named after the Norwegian mathematician Niels Henrik Abel. It describes a system where you can swap the order of two things and get the same result, so 'order does not matter', for example 'a plus b equals b plus a'.