Installation of Imac OS

Sadly if there is no disk present, then it has it is either not formatted correctly or has failed.

To find out for sure, go back to Disk Utility and see if you can reformat the disk as per the erase instructions.

Connect the iMac directly to your router using an Ethernet cable and use (Command-R) for Internet Recovery Mode.

Then follow the Erase and Install directions at > https://support.apple.com/en-us/HT204904

When you erased the Macintosh HD drive, did you specify an APFS file system (not case-sensitive), with a GUID partition scheme? This is what Mojave and later expect for partition type for a compatible installation. I suggest you go back and try the erase again.

If macOS Utilities was accessed previously to wipe the drive, then apparently the Mac can boot to the Recovery partition. I suggest you attempt to restart the Mac again with the Command-R key combination.

Restart the Mac. When you hear the startup chime press the ⌘R keys and hold until you see the Apple logo and progress bar.

If you continue to only startup to the Internet recovery screen (with the globe) and get a failure error, try connecting your Mac to your router with an ethernet cable, or move the Mac closer to the router if using wi-fi. The ethernet cable option is probably better than wi-fi.

Once you have successfully started in recovery mode, follow the good guidance posted by @ VikingOSX above.

trying to register my imac 7.1 but no luck

You’re welcome.