A classification of semifield planes of order q4 with kernel Fq2 and center Fq is given. For q an odd prime, this proves the conjecture stated in [M. Cordero, R. Figueroa, On the semifield planes of order 54 and dimension 2 over the kernel, Note Mat. (in press)]. Also, we extend the classification of semifield planes lifted from Desarguesian planes of order q2, q odd, obtained in [M. Cordero, R. Figueroa, On some new classes of semifield planes, Osaka J. Math. 30 (1993) 171–178], to the even characteristic case.
Semifield planes of order q^4 with kernel GF(q^2) and center GF(q) / Cardinali, I.; Polverino, O.; Trombetti, Rocco. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 27:(2006), pp. 940-961.
Semifield planes of order q^4 with kernel GF(q^2) and center GF(q)
TROMBETTI, ROCCO
2006
Abstract
A classification of semifield planes of order q4 with kernel Fq2 and center Fq is given. For q an odd prime, this proves the conjecture stated in [M. Cordero, R. Figueroa, On the semifield planes of order 54 and dimension 2 over the kernel, Note Mat. (in press)]. Also, we extend the classification of semifield planes lifted from Desarguesian planes of order q2, q odd, obtained in [M. Cordero, R. Figueroa, On some new classes of semifield planes, Osaka J. Math. 30 (1993) 171–178], to the even characteristic case.| File | Dimensione | Formato | |
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