A group homomorphism with this property preserves the order of group elements.
A group homomorphism with this property preserves the order of group elements. If a functor exhibits this property when restricted to morphisms with common domains and ranges, then the functor is faithful. Checking for a trivial kernel is an easy way to show that a group homomorphism or a linear transformation has this property. A function f exhibits this property if f-of-a equals f-of-b implies that a equals b. Restricting the domain of f-of-x equals x-squared to all positive numbers forces this condition upon f. When paired with surjectivity, this property, which is both necessary and sufficient for a function to be invertible, makes a function bijective. For 10 points, functions with what property pass the horizontal line test?
A group homomorphism with this property preserves the order of group elements.
injective [or one-to-one; prompt on monomorphism]