- #1
bentley4
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According to wiki:
"a non-abelian group, also sometimes called a non-commutative group, is a group (G, * ) in which there are at least two elements a and b of G such that a * b ≠ b * a."
I thought in order to be an abelean group, 5 axioms must be satisfied. If one of them is not satisfied it would logically be a non-abelean group. Then why is it only called non-commutative group? Is this just a bad name or do I misunderstand?
"a non-abelian group, also sometimes called a non-commutative group, is a group (G, * ) in which there are at least two elements a and b of G such that a * b ≠ b * a."
I thought in order to be an abelean group, 5 axioms must be satisfied. If one of them is not satisfied it would logically be a non-abelean group. Then why is it only called non-commutative group? Is this just a bad name or do I misunderstand?