My computer turns on for a few minutes and then it suddenly turns itself off with the message: "authoritysystem." I am not an expert so I have no idea if this is a bug or if someone is hacking me?
You don't provide enough details to tell for sure what the issue is. For example, you don't say the operating system, you don't say if the message is a popup or what happens before, if you are on the Internet, are you behind a firewall, is it configured properly. Are you running uptodate antivirus protection? Several viruses can have the effect of shutting down the system.
One in particular is the w32blaster worm. You can read about it on many anti-virus sites. For example, this article describes the worm and tells how to get rid of it. If you are not running up-to-date antivirus and not running a firewall when accessing the Internet, you will continue to have problems.
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