active filter do not require inductor?

Filters require poles and zeros.

You can make poles and zeros in a driving point impedance function with inductors and capacitors. (lumped element filter)

You can make poles and zeros in a gain transfer function with an op amp, resistors, and capacitors (i.e. active filter)

You can make poles and zeros with transmission line open stubs, shorted stubs, and transmission line thrus (distributed filter)

Yes, of course correct.
May I add (for clarity): The principle behind RC active filtering is frequency-dependent feedback.