We need to install arcgis server and desktop on a system which is having ip address and not a fully qualified domain name. Is it mandatory to have a fully qualified domain name for arcgis server installation for arcgis portal. Dosen't arcgis portal work on static public ip address.
There's no problem installing Portal, Server, or Data Store on a machine where the hostname is the IP address. It's actually what the AWS CloudFormation templates do. I would expect your system to have both a public IP address but also an internal IP address. You can set everything to use the internal IP address, but I imagine the machine has some type of hostname, even if it's in a workgroup. You can let everything pick up the local hostname and then just make sure you have your public DNS name mapped to the public IP address so you can register the Web Adaptor or whatever you'll be using.