Consider: A. A group can have zero elements. B. A group cannot have any idempotent element except the identity. C. An isomorphism from a group ⟨G, *⟩ to ⟨G, *⟩ is called an automorphism. D. If every element in a group is its own inverse, the group must be abelian.

1. AB,C and D are correct
2. BOnly A and C are correct
3. COnly B and C are correct
4. DAll A, B, C and D are correct.

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Correct answer: A. B,C and D are correct

Explanation

A group contains at least the identity (A false). a·a = a forces a = e (B true). An isomorphism of a group onto itself is an automorphism (C true). If x = x⁻¹ for all x, then ab = (ab)⁻¹ = b⁻¹a⁻¹ = ba (D true).