Hi,
To control an induction cooker element you need IGBT type control and current monitoring.
The induction element is designed for 25kHz to 50kHz, much higher frequencies than 50/60Hz, so its impedance will be much lower at 50/60 than at the higher frequencies.
So you will have the rest of the control and power drive circuit.
Look at it and google the part numbers, this will give you an insight into how the element is powered.
Here is one that I repaired for my boss about 3 months ago.
It is for two elements and has extensive filtering to ensure a clean/no-interference operation.
Google:
how induction cooktops work
Tom... 
