Re: Hide Groups widget
Something like this should work (or at least get you going in the right direction:
And further reading on conditional tags:
https://codex.wordpress.org/Conditional_Tags
ETA: oops, I assumed that the “blog” page was your index. In my pastebin example, you just want to replace the text “Your index page title” with the title of the page you DO NOT want the widget showing up on. Or, I guess you could also get rid of the exclamation mark and insert the title of the page that you DO want the widget on. If you literally only have the one BP page and one blog page, either method should work.