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{\bf Nick Gill}
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{\bf Nilpotent Singer Groups}
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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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