Why is it that when I install Ubuntu with a user name, a new group is created with that name too?
Is there a reason we're not just plain Administrators?
Being an administrator just opens up a bunch of other options to you as a user (they are mostly unimportant), but it won't really change anything.
By default, the first user (the one you create from the installer) is an administrator (essentially) with some options disabled for safety. The reason everyone gets a separate group is simply because it makes it easier to manage permissions (on a Unix) system in this way.
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This is necessary because of Linux file system rights. Linux (and other Unix variants) have a right setting for 3 types of users: a owner, a owning group and "others" (i.e. someone who's not the owner and not in the owning group). All files (on linux filesystems) are obliged to have a owner and owning group.
Since usually files that are created by a user are meant for that user only the owner is set to the user and the owning group is set to a special group the user belongs to: the group with the user its name. Thats why such a group is created whenever a new user is created.
There is you, root (admin), and everyone else. You're automatically added to sudoers and can perform as root(admin) via sudo because of your group status. Root and Administrator are pretty synonymous.
Ubuntu wants to make it easy for users to get up and running without having to install and configure all that stuff.
EDIT: Read RootSudo
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