Like the title describes I have a user who is assigned full permissions but when I click on on the user groups I get a permissions error "You do not have permission to view the membership of the group".
Site Actions ->
Site Settings ->
People and Groups ->
[From the list of the left, select the group which you want] ->
Group Settings ->
Make sure that "Who can view the membership of the group?" is set to "Everyone" ->
Make sure that "Who can edit the membership of the group?" is set to "Group Members"
Step 1: Create a group with Full Control permission level (for example, name is Group1). Let's say Group2 is the group that needs users to be added/removed.
Step 2: Under Group Settings, add Group1 as the Group Owner of Group2 (this is possible). Now all members of Group1 will be able to add/remove users to/from Group2.
Hope this makes sense.