Mathematics · Group Theory
For a group G, let Aut(G) denote the group (under composition) of all bijective group homomorphisms from G onto itself. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If G is finite, then Aut(G × G) is always finite.
- 2If G is the group of complex numbers under addition, then Aut(G) is non-abelian.✓
- 3If |G| = 2, then Aut(G × G) is abelian.
- 4If G1 and G2 are two groups such that Aut(G1) is isomorphic to Aut(G2), then G1 must be isomorphic to G2.
Correct answer
If G is the group of complex numbers under addition, then Aut(G) is non-abelian.
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