Some sporadic translation planes of order 11^2


In \cite{PK}, the authors constructed a translation plane \Pi of order 11^2 arising from replacement of a sporadic chain F' of reguli in a regular spread F of PG(3,11). They also showed that two more non isomorphic translation planes, called  \Pi_1 and \Pi_{13}, arise respectively by derivation and double derivation in F\setminus F' which correspond to a further replacement of a regulus with its opposite regulus and a pair of reguli with their opposite reguli, respectively.  In \cite{AL}, the authors proved that the translation complement of \Pi contains a subgroup isomorphic to \SL(2,5). Here, the full collineation group of each of the planes \Pi, \Pi_1 and \Pi_{13} is determined.

DOI Code: 10.1285/i15900932v29n1supplp121

Translation plane; Replacement; Collineation; Chain of circles

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