Title: A General Existence Result for Translation Subplanes

Abstract: A subplane of a projective plane is a subset of the set of points and lines that is itself a projective plane. In this talk we introduce conditions on an elation group of a projective plane that guarantee the existence of translation subplanes. Time permitting, we will see how the base case of our theorem extends a well-known result on the existence of Abelian elation groups to a result on the existence of Desarguesian subplanes. No prior knowledge of geometry is required.