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If your groups and categories have exactly the same name, you could try modifying your group home.php file (groups/single/home.php in the bp-default theme), accessing the group name and using that in a query_posts / have_posts loop

If they have different names, you will have to look at extending your group, adding a parameter to capture the corresponding category id. Again, you would then add a query_posts / have_posts loop and use it your group home.php template.

This page gives some more information on the groups API, and may be of some help: https://codex.buddypress.org/developer-docs/group-extension-api/