A one-one mapping of a finite group onto itself is called an automorphism.

Definition of an Automorphism:
An automorphism of a group is an isomorphism from the group to itself. In other words, it is a mapping of the group elements onto itself that preserves the group structure.

Explanation:
Let's break down the options and understand why the correct answer is option 'C' (automorphism).

a) Isomorphism:
An isomorphism is a bijective homomorphism, which means it is a mapping between two groups that preserves the group structure and is one-to-one and onto. While a one-one mapping of a finite group onto itself is certainly a one-to-one function, it may not necessarily be onto. Therefore, the correct answer is not isomorphism.

b) Homomorphism:
A homomorphism is a mapping between two groups that preserves the group operation. In other words, if we have two groups G and H, a homomorphism φ: G → H satisfies φ(ab) = φ(a)φ(b) for all elements a, b in G. While a one-one mapping of a finite group onto itself is certainly a one-to-one function, it may not necessarily preserve the group operation. Therefore, the correct answer is not homomorphism.

c) Automorphism:
As mentioned earlier, an automorphism is an isomorphism from a group to itself. It is a one-to-one and onto mapping that preserves the group structure. Since the given mapping is one-one (injective), it is a one-to-one mapping. Since it is a mapping of the group onto itself, it is onto (surjective). And since it is a mapping that preserves the group structure, it is a homomorphism. Therefore, the correct answer is automorphism.

Summary:
A one-one mapping of a finite group onto itself is called an automorphism. It is a one-to-one and onto mapping that preserves the group structure. Therefore, the correct answer is option 'C' (automorphism).