how do you block it it keeps popping up on my computer, i do not want it and i keep having to hold down f5.

Do you have another PC in the house that has network sharing enabled, and a defined home group?

This may help - Windows 8 Homegroup Topics

no i don't this is the only one with network, i didn't install it nor do i want it.

Is the message prompting you to "Join" a home group? Windows 8.1 automatically creates one if none exists. So, I can't think of any reason that it would prompt you for anything.

i just keep getting an icon on my desktop cannot move it to recycling bin, cannot delete it, i didn't even join it.

Apparently many folks are having this issue - see if the directions on the following page resolve the problem.

Remove Homegroup icon appearing suddenly on Windows 8 desktop

thank you very much i will try that.