Final answer:
The Supreme Court's decision in Gregg v. Georgia established certain criteria for a state's death penalty to be considered constitutional. Trial by jury is not one of these criteria. The correct option is d.
Step-by-step explanation:
The correct answer is d. Trial by Jury. In the Supreme Court's decision in Gregg v. Georgia, the Court held that a state's death penalty must meet certain criteria to be considered constitutional.
These criteria include a bifurcated trial process, presentation of mitigating factors, and appellate review. However, the Court did not specifically require a trial by jury as an element of a state's death penalty.
Therefore, trial by jury is not an element of a state's death penalty that must exist to be constitutional. The correct option is d.