Step 1: Understanding the Concept:
Moving left to right in a period, the nuclear charge increases while the electrons are added to the same shell. The pull on the outer electrons grows, so the radius drops.
Step 2: Detailed Explanation:
Among the groups 15, 16, 17 and 18, group 17 (the halogens) shows the smallest covalent radius in each period. Group 18 is a special case: noble gases are listed by van der Waals radius, which is larger, so they are not counted as the smallest.
Step 3: Check the options.
Groups 15 and 16 come earlier in the period, so their radii are larger than those of group 17.
Final Answer:
Group 17 has the smallest atomic radii, option (C).
\[ \boxed{\text{Group 17}} \]