I have installed the BuddyPress plugin and as a user can't seem to be able to create a Group. If I go to mydomain.com/members/my-username/groups/ I don't see a link to Create Groups. But if I hand-type the Create at the end of this link: mydomain.com/members/my-username/groups/create it displays it. I think something is missing in the core perhaps. I looked for some answers here but I could not find anything that addresses this issue.
Go to .../wp-admin/admin.php?page=bp-settings. Is this option selected?
Enable group creation for all users
If it is, then try switching to a WP theme like 2013. If the button appears, then the issue is in your theme.
edit:
BuddyPress doesn't provide a Create link on member profile pages. mydomain.com/members/my-username/groups/
The link will be here: mydomain.com/groups/
You can add a link, but how you add it depends on exactly where you want it to appear.