term:

Primogeniture

primogeniture n

1 : the state of being the firstborn of the children of the same parents
2 : exclusive right of inheritance
;specif
: a right to take all the real property of an estate belonging under English law to the eldest son or eldest male in the next degree of consanguinity if there is no son of an ancestor to the exclusion of all female and younger male descendants

Source: Merriam-Webster's Dictionary of Law ©1996. Merriam-Webster, Incorporated. Published under license with Merriam-Webster, Incorporated.