Not enough information, I’m afraid.

Are you trying to add the Sonos One Sl as a separate ‘room’, using the ‘add a device’ function, or as one of a pair of surround speakers?

What router do you have? 

Is the Sonos One connecting when you’re using the Ethernet cable, but not when you remove the cable?

What channel and frequency is your Arc connected to?

Trying to add it to same room where sub and arc are located.

verizon G3100 router 

correct-sl one connects with Ethernet but disconnects when trying to connect via WiFi 

 channel 11 for arc and sub -20MHZ frequency 

Are trying to bond 1 or two One SL's to Arc? Because you cannot bond only 1 surround speaker. You need to have two, configured as two "rooms” in Sonos. 

Two. Did that already —the issue is it’s not connecting to WiFi 

As stated by @106rallye , you can’t add two more speakers in the ‘room’ for the Sonos Arc. You can only ‘bond’ surround speakers to that ‘room’. In order to add a pair of speakers, you need to set them up in a separately named ‘room’ in the Sonos controller. Physically, you can put them anywhere, of course, just in the Sonos software they have to be in a separate ‘room’. 

Is ARC wired or wireless? In any case do not disable ARC’s wireless.

 arc and sub room1 & room 2 is where I’m trying to hook up sl one’s but not having any luck getting it to sync with WiFi 

Is this Verizon router wired, or is it a hotspot/LTE/4G/5G router? Have you checked the network requirements?

And have you tried rebooting the router?

I’d also be tempted to wire one of the other speakers, and run the network as a ‘wired’ network, to get around these potential issues.