Nilpotent Singer groups

Gill, Nick (2006). Nilpotent Singer groups. Electronic Journal of Combinatorics, 13(1) R94.

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

Item Type:	Journal Article
Copyright Holders:	2006 The American Mathematical Society
ISSN:	1077-8926
Academic Unit/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	28187
Depositing User:	Nick Gill
Date Deposited:	16 Feb 2011 12:48
Last Modified:	16 Feb 2011 20:11
URI:	http://oro.open.ac.uk/id/eprint/28187

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