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Definition: If a permutation representation G -> Perm (S) is injective, then the corresponding operation is faithful. To be faithful, an operation must have the property that m_g, multiplication by g, is not the identity map unless g is the identity. In other words, an operation is faithful if it has the property: The only element g of G such that gs = s for every s in S is the identity.
Source: Algebra, second edition by Michael Artin