“In mathematics, an abelian group, also called a commutative group, is a group[1] in which the result of applying the group operation to [any] two group elements does not depend on the order in which they are written. That is, the group operation is commutative[2]” (“Abelian Group,” Wikipedia, retrieved 12/15/2020, bold added for emphasis). One of the best known Abelian groups is the set of real numbers paired with the binary operation[3] of addition (ibid).
“A group in which the group operation is not commutative is called a ‘non-abelian group’ or ‘non-commutative group'” (ibid).
The group operation of an Abelian group is often denoted with a plus sign (“+“), as opposed to a multiplication sign (“*”) or no sign (ibid). Abelian groups are also sometimes referred to as abelian groups (note the lowercase “a”) (ibid).
- [1] See “What is the Gist of a “Group” (Group Theory)?”
- [2] See “What is the Gist of “Commutativity” (Mathematics)?”
- [3] See “What is the Gist of a “Binary Operation”?”
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
