Washing Machine Drain- vent needed?

My washing machine (laundry) drains into a concrete tub currently, this tub connects into the drain pipe that comes down from the kitchen sink, there is a vent up from the kitchen sink drain out the roof. After the laundry tub the pipe goes down under the slab and over to the main. I'm planning to finish the laundry and wanted to put the drain directly into a 2" pipe that would include a trap and then T into the pipe that comes down from the kitchen.
I'm wondering if I'd need a separate vent for this set-up just for the washer? If necessary could I use one of those vent valves (Studor)?

I believe if the wm drain hose terminates to open air; that is, if it terminates in the tub, you don't need to vent it.

There's no direct connection to the sewer, so you don't need a trap. Because the drain is not directly connected to any traps, there's no need to have a vent.

What I'm talking about is actually putting the wash. machine drain hose directly into a drain pipe, that would include a trap.
That's why I'm wondering if I need a vent?
Like I said I guess it wouldn't hurt to use a studor.

A pro will chime in, but I'm pretty sure that you WILL need a vent if you go directly into the tub drain. In fact, I'm doubtful an AAV will be sufficient, because of the velocity and volume of water ejected by the washer.

If you cut a tee into the kitchen waste in the basement,
yes, you will need to vent it.

A studor will work for that.
Or it could have been hard vented in at 42" above the 2nd floor with a revent.

Without the vent, the kitchen above can siphon away your trap seal in the basement.

vent

Even with a Studor, the water comng down from the sink could "push" the water out of the trap under certain circumstances.

I look into the Studor, I know there's restrictions like not closing it in behind a wall. But might be the best option though since getting a vent out would require a lot of demolition.

One other issue related to this. The pipe coming down from the kitchen is steel (looks like galvanized), it doesn't leak or look rusty.

Wonder how long something like that will last?
The house was built in 1957 and I assume this is original. It goes into the floor into a cast iron.

If I did try to replace my issue would be how to deal with where it connects to the cast iron?