Mathematics · Group Theory
An abstract algebra student is evaluating a group homomorphism map φ : G → G', where e' is the identity element of the target group G'. The student calculates a subset defined as the set of all elements in G that map directly to e'. Based on the mathematical properties of group homomorphisms, what is the structural classification of this evaluated subset?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It is always a normal subgroup.✓
- 2It is an alternating group consisting of even permutations.
- 3It is an integral domain with no zero divisors.
- 4It is a conjugacy class of size 1 within the center.
Correct answer
It is always a normal subgroup.
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