Mathematics · Group Theory
Which of the following conditions does NOT necessarily imply that a group G is abelian?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The center of G is equal to G (Z(G) = G)
- 2The order of G is a prime number
- 3There exists an element a ∈ G − {e} such that ax = xa, ∀x ∈ G✓
- 4Every element in G has order 2
Correct answer
There exists an element a ∈ G − {e} such that ax = xa, ∀x ∈ G
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