Hi!
First you start an extrude on either one of the surfaces of the cylinder or on a datum plane. From there you would sketch out the profile of the groove. Mine is shown below...
Once you have completed your sketch, you click the green check mark to go back ot the extrude. By selecting Remove Material (shown below) the groove will be removed from your cylinder.
From there all you have to do is click the green checkmark to finish the extrude.
Does this solve your problem?