All the information on the internet I can find about frying a turkey outdoors involves a propane burner. Wouldn't a portable induction stove be safer, because there is no flame?
I recognize that I would need a more expensive stainless steel pot than the more common aluminum ones. Are there any other limitations that I would run into?
Sheer power is an issue.
The lowest-power "turkey fryer" models I can find are 38000 BTU (example). That's equal to 10500 Watts.
It's true that induction is far more efficient than flame-base burners (90% energy transfer for induction vs. 40-55% for gas/propane, we'll call it a factor of two for simplicity), but that doesn't really help much. Let's say we need 5250 Watts of electric power to an induction burner - that's almost 22 amps at 240 volts, so it would need to plug into a 30 amp receptacle on a 30 amp circuit.
To a rough approximation, nobody has outdoor 30A / 240V receptacles. Maybe a few RV owners, but that's about it. Adding such a thing to an existing home would cost hundreds if not easily a thousand dollars (parts and labor) in the US today. A 20lb propane tank is about $50.
The standard electrical receptacle (that mass-market appliances can design for, without requiring purchasers to perform upgrades) in the US is only 15A at 120V - good for about 1800 Watts. Considering efficiency, that's equal to about a 12000 BTU burner - less than a third of the power of the propane unit.
In 240V-land, things are a little better: call it 15A (picking an average between UK 13A and continental 16A) at 240V for 3600 Watts, equal to a 25000 BTU burner. Still only two-thirds of the power of the propane unit, though.
Safety is another consideration. Not that a turkey-sized vat of hot oil is ever going to be "safe", but at least the short hose on the propane burners means the tanks must be located very close to the burner so there's no tripping hazard. An electrical cord running back to a receptacle presents a tripping hazard and risks spilling the vat of hot oil if it gets pulled.
An electrical cord obviously also tethers you to a building, in a way that a standalone tank and burner do not. All things being equal, an electric setup is probably going to end up closer to buildings (especially since it needs to be an expensive, high-power cord).
By the way, 38000 BTU is the smallest fryer I could find. 80000 BTU, 100000 BTU, and 200000 BTU apparently exist and those are never going to be matched by electric (at least for home use, power feeds that large could exist in commercial/industrial setups).
There's no reason you can't use a portable induction ring, as long as you can find one with the power to heat up a big pot of oil and keep it at the right temperature.
The challenge you'll have is equipment. The problem is size, the pots for frying turkeys are pretty big, often far bigger than the portable induction rings out there. Often they cover the controls, which is bad because you can't adjust the power without moving a very big, heavy pot full of oil. Also the heat from the pot can fry the electronics and ruin the ring. You'd need to find an induction ring where the controls aren't going to be at risk from the pot, and you can reach them.
