Innovations in Incidence Geometry

On the autotopism group of the commutative Dickson semifield $K$ and the stabilizer of the Ganley unital embedded in the semifield plane $\Pi(K)$

Alice M. W. Hui, Yee Ka Tai, and Philip P. W. Wong

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Abstract

Two methods, one algebraic and one geometric, are given to determine the autotopism group of the commutative Dickson semifield, completing a result of Sandler. The collineation stabilizer subgroup of the embedded Ganley unital is exhibited as a semidirect product whose factor groups are semidirect products of abelian groups.

Article information

Source
Innov. Incidence Geom., Volume 14, Number 1 (2015), 27-42.

Dates
Received: 16 August 2013
Accepted: 19 March 2014
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323026

Digital Object Identifier
doi:10.2140/iig.2015.14.27

Mathematical Reviews number (MathSciNet)
MR3450950

Zentralblatt MATH identifier
1404.51002

Subjects
Primary: 12K10: Semifields [See also 16Y60] 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX] 51A35: Non-Desarguesian affine and projective planes 51B10: Möbius geometries 51E05: General block designs [See also 05B05]

Keywords
Dickson semifield semifield plane autotopism group stabilizer of the embedded Ganley unital automorphism group of unitary block design inversive plane

Citation

Hui, Alice M. W.; Tai, Yee Ka; Wong, Philip P. W. On the autotopism group of the commutative Dickson semifield $K$ and the stabilizer of the Ganley unital embedded in the semifield plane $\Pi(K)$. Innov. Incidence Geom. 14 (2015), no. 1, 27--42. doi:10.2140/iig.2015.14.27. https://projecteuclid.org/euclid.iig/1551323026


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