Exercise · ZW-ABELIAN-GROUP-009 · ★★☆ Intermediate
Select the only abelian group with its usual operation.
Choose one option.
Show answer
- A. (ℝ,+)
Explanation
(ℝ, +) is abelian because a + b = b + a for all reals. (ℕ, +) is not a group (it has no inverses), GL₂(ℝ) under multiplication is not commutative, and S₃ under composition is not either.
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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