Nilpotent Singer Groups

Let N be a nilpotent group normal in a group G. Suppose that G acts transitively upon the points of a finite non-Desarguesian projective plane P. We prove that, if P has square order, then N must act semi-regularly on P. In addition we prove that if a finite non-Desarguesian projective plane P admits more than one nilpotent group which is regular on the points of P then P has non-square order and the automorphism group of P has odd order.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Nick Gill
• Keywords: COMBINATORICS 2006, Finite Non-Desarguesian Projective, Nilpotent Group, Non-Desarguesian Projective Plane