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The lock cylinder in a 1981 steering column should be held in place by a separate screw. The screw is located in the column head and goes through a notch in the cylinder. Before 1979 the lock cylinder had a spring loaded steel
wedge that engaged a slot in the steering column head. Thiefs were able to use a slam puller to dislodge the lock cylinder and steal the car. In 1979 the steering column and lock cylinder were changed to a screw retained design.
Are you sure you have the correct lock cylinder? The GM part number for the correct screw retained cylinder is 7830380.