for the purpose of executing such scheme

The federal mail fraud statute does not purport to reach all frauds, but only those limited instances in which the use of the mails is a part of the execution of the fraud, leaving all other cases to be dealt with by appropriate state law. ... only if the mailings were 'a part of the execution of the fraud,' or ... were 'incident to an essential part of the scheme,' do they fall within the ban of the federal mail fraud statute.

Defined by the Supreme Court in - Parr v. United States, 363 U.S. 370 (1960).