publication . Article . Preprint . 2006

Nilpotent Singer Groups

Gill, Nick;
Open Access English
  • Published: 10 Jun 2006
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 $\mathcal{P}$.\ud 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.
Subjects
free text keywords: 20B25, 51A35, Mathematics - Combinatorics, Mathematics - Group Theory

[CP93] Alan R. Camina and Cheryl E. Praeger, Line-transitive automorphism groups of linear spaces, Bull. London Math. Soc. 25 (1993), 309{315.

[Dem97] P. Dembowski, Finite geometries, Springer-Verlag, 1997.

[Ho98] [Wag59] A. Wagner, On perspectivities of nite projective planes, Math. Z. 71 (1959), 113{123.

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 $\mathcal{P}$.\ud 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.
Subjects
free text keywords: 20B25, 51A35, Mathematics - Combinatorics, Mathematics - Group Theory

[CP93] Alan R. Camina and Cheryl E. Praeger, Line-transitive automorphism groups of linear spaces, Bull. London Math. Soc. 25 (1993), 309{315.

[Dem97] P. Dembowski, Finite geometries, Springer-Verlag, 1997.

[Ho98] [Wag59] A. Wagner, On perspectivities of nite projective planes, Math. Z. 71 (1959), 113{123.

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . Preprint . 2006

Nilpotent Singer Groups

Gill, Nick;