Step 1: Elements of a state in political theory.
A state requires population, territory, government, and sovereignty. Of these, {sovereignty}—supreme authority internally and independence externally—is decisive.
Step 2: Why others are not “elements.”
Flag, capital and traditions are important symbols/institutions, not constitutive elements.
Step 3: Conclude.
\[
\boxed{\text{Sovereignty (Option C) is the most vital element.}}
\]