High Quality Content by WIKIPEDIA articles! In mathematics, a translation plane is a particular kind of projective plane, as considered as a combinatorial object. In a projective plane, scriptstyle p represents a point, and scriptstyle L represents a line. A central collineation with center scriptstyle p and axis scriptstyle L is a collineation fixing every point on scriptstyle L and every line through scriptstyle p. It is called an "elation" if scriptstyle p is on scriptstyle L, otherwise it is called a "homology". The central collineations with centre scriptstyle p and axis scriptstyle L form a group. A projective plane scriptstyle Pi is called a translation plane if there exists a line scriptstyle L such that the group of elations with axis scriptstyle L is transitive on the affine plane ?l (the affine derivative of ?).

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