Exercise · ZW-ABELIAN-GROUP-002 · ★☆☆ Basic
Which is an abelian group?
Choose one option.
Show answer
- D. (ℤ, +)
Explanation
(ℤ, +) is abelian because a + b = b + a. S₃ (permutations of three elements) does not commute, (ℤ, ·) is not even a group and (ℕ, −) neither.
Review the concept: Abelian group
A group is abelian, or commutative, if its operation allows the order of any two elements to be swapped.
\[a\ast b=b\ast a \quad \forall a,b\in G\]
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