Semifields of order with left nucleus and center |
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| Authors: | Norman L Johnson Giuseppe Marino Olga Polverino Rocco Trombetti |
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| Institution: | aMathematics Department, University of Iowa, Iowa City, IA 52242, USA;bDipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, I-80126 Napoli, Italy;cDipartimento di Matematica, Seconda Università degli Studi di Napoli, I-81100 Caserta, Italy |
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| Abstract: | In G. Marino, O. Polverino, R. Trombetti, On  -linear sets of PG(3,q3) and semifields, J. Combin. Theory Ser. A 114 (5) (2007) 769–788] it has been proven that there exist six non-isotopic families  (i=0,…,5) of semifields of order q6 with left nucleus  and center  , according to the different geometric configurations of the associated  -linear sets. In this paper we first prove that any semifield of order q6 with left nucleus  , right and middle nuclei  and center  is isotopic to a cyclic semifield. Then, we focus on the family  by proving that it can be partitioned into three further non-isotopic families:  ,  ,  and we show that any semifield of order q6 with left nucleus  , right and middle nuclei  and center  belongs to the family  . |
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| Keywords: | Semifield Isotopy Linear set |
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