Administrators (commonly known as sysops or admins) on the AoPSWiki have certain powers which are not granted to ordinary users.
Administrators have easy one-click rollback abilities to revert the previous user's moves; however, the rollback ability is generally only used to revert vandalism. If the revert is of a legitimate edit, then no useful edit summary is left and the revert may be seen as abusage of admin powers.
They have the power to permanently delete articles beyond the average user's ability to restore, though administrators can restore these deleted articles. As a direct result, they can also move articles to the location of other already-existing articles by simply deleting the other one.
Administrators have access to Special:Unwatchedpages, a list containing all of the articles on the wiki which aren't being watched by users. This is to minimize the amount of damage that can be potentially done by a vandal. Sysops also have access to certain other special pages.
There is also a protection ability in which articles subject to vandalism or other disputes can be locked from editing. Articles can be semi-protected, which bans new users from editing that article. They can also be fully-protected, which then only lets other sysops to edit. There are similar protection abilities against page moves to prevent page-move vandalism.
Administrators also can block (prevent from editing all of the wiki except their own user page and user talk page) or ban (prevent from logging in) any user.
Mostly only the administrators of the AoPS forums and certain moderators on the AoPS forums are administrators.
A bureaucrat is a special type of administrator with the ability to make users into sysops and other bureaucrats. Mostly only forum administrators are bureaucrats on the AoPSWiki.
Bureaucrats have access to Special:Userrights, where they edit user permissions.
List of sysops
List of bureaucrats