Nilpotent Singer Groups

Nick Gill

Abstract


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 ${\cal P}$. We prove that, if ${\cal P}$ has square order, then $N$ must act semi-regularly on ${\cal P}$.

In addition we prove that if a finite non-Desarguesian projective plane ${\cal P}$ admits more than one nilpotent group which is regular on the points of ${\cal P}$ then ${\cal P}$ has non-square order and the automorphism group of ${\cal P}$ has odd order.


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