A bit of background: in Linux, a user is always a member of a primary group and also can be a member of zero or more of secondary groups.
When a user creates a file, the file's user ID and group ID are set to the ID of the user and her primary group respectively, so the file becomes "owned" by that user and group. Also, permissions on the file are set automatically using the current umask setting, which includes permissions for "user", "group" and "others". So, more or less, all users in the same group as user's primary group are getting at least some permissions on the files the user creates.
Secondary groups, on the other hand, do not affect ownership of the files user creates, you can think of them as a way to allow access to files created by others.
As you can see, the "automatic" behavior of the primary group makes it a bit prone to allowing access unintentionally. For this reason, Ubuntu along with many other Linux distributions uses User Private Group scheme - when a user is created, a group with the same name is created and is set as the primary group of that user. So the user's primary group is always a group with exactly one member.
From CentOS documentation:
Red Hat Enterprise Linux uses a user private group (UPG) scheme, which
makes UNIX groups easier to manage.
A UPG is created whenever a new user is added to the system. A UPG
has the same name as the user for which it was created and that user
is the only member of the UPG.
UPGs make it safe to set default permissions for a newly created file
or directory, allowing both the user and the group of that user to
make modifications to the file or directory.
The setting which determines what permissions are applied to a newly
created file or directory is called a umask and is configured in the
/etc/bashrc file. Traditionally on UNIX systems, the umask is set to
022, which allows only the user who created the file or directory to
make modifications. Under this scheme, all other users, including
members of the creator's group, are not allowed to make any
modifications. However, under the UPG scheme, this "group protection"
is not necessary since every user has their own private group.
So, as you can see, there's no "user is a member of another user" thing - as @Kent mentions, in Linux users cannot "contain" other users and also groups can not be nested and can only contain users, not other groups. The source of your confusion is that within User Private Group scheme user's primary group is a "private" group with the same name as the user.