Dagger Definitions
Part I —
Part II —
Update of Jan. 2, 2011 —
Singer goes on to say that "A finite projective plane, PG (2, pn ), defined in this way is Pascalian and Desarguesian ; it exists for every prime p and positive integer n , and there is only one such PG (2, pn ) for a given p and n …."
His definitions therefore deliberately exclude non -Desarguesian finite projective planes, which were known to exist at the time he wrote.