In the periodic table, elements in group 17 (Group VIIA) are known as the halogens. They include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).

The halogens are known for their tendency to form ions with a charge of -1 by gaining one electron to complete their valence shell. For example, fluorine typically forms the fluoride ion (\(F^-\)), chlorine forms the chloride ion (\(Cl^-\)), and so on.

However, the question asks which element cannot show variable oxidation states. Variable oxidation states refer to the ability of an element to exhibit multiple oxidation states in its compounds.

Among the halogens, chlorine, bromine, and iodine are capable of exhibiting variable oxidation states, while fluorine typically exhibits an oxidation state of -1 in its compounds. Fluorine is highly electronegative and strongly prefers to gain one electron to achieve a stable octet configuration.

Therefore, the correct answer is (b) Fluorine.