Exercise · ZW-ABELIAN-GROUP-007 · ★★☆ Intermediate
If in a group G there are elements a and b with a∗b ≠ b∗a, what can be concluded?
Choose one option.
Show answer
- C. G is not abelian
Explanation
Abelian requires every pair to commute, so a single pair that does not commute is enough for G not to be abelian. It does not affect G being a group (S₃ is a group and is not abelian) and says nothing about its size.
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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