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A group action is called faithful when its kernel is exactly the singleton set containing only the identity element of $G$, i.e., $\{g \mid ga = a\} = \{1\}$.

Conditions: The action has a kernel as defined in the video.; $\{1\}$ denotes the singleton containing the identity element of $G$.

A group action is called faithful when its kernel is exactly the singleton set containing only the identity element of $G$, i.e., $\{g \mid ga = a\} = \{1\}$.

Conditions: The action has a kernel as defined in the video.; $\{1\}$ denotes the singleton containing the identity element of $G$.