Vol. 14, No. 1, 2015

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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

Vol. 14 (2015), No. 1, 27–42

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.

Dickson semifield, semifield plane, autotopism group, stabilizer of the embedded Ganley unital, automorphism group of unitary block design, inversive plane
Mathematical Subject Classification 2010
Primary: 12K10, 20B25, 51A35, 51B10, 51E05
Received: 16 August 2013
Accepted: 19 March 2014
Alice M. W. Hui
Yee Ka Tai
Philip P. W. Wong