Double-Y syndrome is a genetic mutation present in some males in the 22nd century. Specifically, it is a deformity of the X/Y chromosome pair, resulting in the YY pattern. This pattern gives the afflicted person (who, by definition, will always be male) a predisposition for antisocial behavior, specifically very brutal crimes, including rape and serial murder of women.
Owing to their dangerous nature, double-Y syndrome convicts are typically detained in separate facilities from other convicted criminals. One such double-Y prison facility was the Fiorina 161 Class C Work Correctional Unit, which originally housed five thousand inmates, all double-Y syndrome sufferers.
Behind the Scenes
It seems perhaps strange that double-Y syndrome criminals are summarily imprisoned for their crimes as they are in Alien3. As the condition is a genetic deformity that gives an individual a predisposition for violent crimes, it would logically follow that the afflicted may not be consciously responsible for the criminal acts they commit, and therefore should not be punishable by law. However, it remains to be seen if the YY Syndrome is the sole cause of the crimes the inmates in Alien3 have committed, or whether it is possible for someone with the syndrome to live a completely crime-free life. The latter seems likely, as prior to Ripley's arrival at the prison the group has apparently been able to live in harmony for some time, despite their genetic condition.
In real life, a double-Y chromosome does not occur without the maternal X, resulting in the XYY syndrome.