As I was reading answers to this question asking how to change usernames, a suggestion to change of the name of the group was also made in this answer. What is the significance of the groups whose only member is the user with the same name?
This is a "user private group scheme" issue.
In order to allow more flexibility, most Linux systems follow the so-called user private group scheme, that assigns each user primarily to his or her own group. This group is a group that only contains this particular user, hence the name "private group". Usually this group has the same name as the user login name, which can be a bit confusing.
What does this have to do with UPG?
UPG sets the default umask to 0002 so that group users can write to files. This would be undesirable and dangerous if everyone belonged to one group (like the “users” group in SUSE) — but when each user is in their own group, the additional group permission is moot until you write into an SGID directory.