The Deathly Regiment is an incredibly secretive statute in wizarding America.
The regulation is carried out by the families of the Elect, who struck a deal with the Generous Ones in order to usurp control of the Lands Below from the native magical practitioners of North America. Every seven years, the Regiment chooses one pureblooded child, "one too young to have a wand," by secret lottery from among its member-families to be sacrificed to the Generous Ones and sent to the Lands Beyond. These children are given a Confederation medallion that may be converted into a kind of Deathly token upon the child's death.
Absalom Thorn died fighting against the Deathly Regiment.
In November of 2009, Alex learned that her half-sister Valeria White was researching the Thorn Family's history and relation to the Regiment with Absalom's reluctant help and the use of a Time-Turner.
In 2010, Mary Dearborn was chosen to be sacrificed, but her sister learned of her fate (possibly through a Mayan Brazier of Visions), and attempted to sacrifice Innocence Pritchard instead; Dearborn was stopped by Alexandra Quick, who rescued Pritchard, and Darla sacrificed herself to save her sister.
In May of 2010, Alex was told the true nature of the Regiment by Tiow. In June of 2010, Alex spoke with Geming Chu about the Regiment, and learned that the Elect chooses a pureblooded child by secret lottery, and that Geming had married a Muggle specifically to protect his children, who, by being half-blooded, would be ineligible for the Regiment's lottery. Alex later spoke with her ancestor Absalom about the Regiment.
The term "regiment" is here used in the sense of a government or regime, as John Knox used it in his 1558 work, The First Blast of the Trumpet Against the Monstrous Regiment of Women.
Theories as to the nature of the Regiment may be posited here.