Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: A generalization of some Huang–Johnson semifields. | A generalization of some Huang-Johnson semifields . Johnson Mathematics Dept. University of Iowa Iowa City Iowa 52242 USA njohnson@math. uiowa. edu Olga Polverino Dipartimento di Matematica Seconda Università degli Studi di Napoli I-81100 Caserta Italy @unina2. it Giuseppe Marino Dipartimento di Matematica Seconda Università degli Studi di Napoli I-81100 Caserta Italy giuseppe. marino @unina2. it Rocco Trombetti Dipartimento di Matematica e Applicazioni Università degli Studi di Napoli Federico II I-80126 Napoli Italy rtrombet@unina. it Submitted May 19 2010 Accepted Jan 25 2011 Published Feb 4 2011 Mathematics Subject Classification 12K10 51A40 51E99 Abstract In H. Huang . Johnson Semifield planes of order 82 Discrete Math. 80 1990 the authors exhibited seven sporadic semifields of order 26 with left nucleus F23 and center F2. Following the notation of that paper these examples are referred as the Huang-Johnson semifields of type II III IV V VI VII and VIII. In N. L. Johnson V. Jha M. Biliotti Handbook of Finite Translation Planes Pure and Applied Mathematics Taylor Books 2007 the question whether these semifields are contained in larger families rather then sporadic is posed. In this paper we first prove that the Huang-Johnson semifield of type VI is isotopic to a cyclic semifield whereas those of types VII and VIII belong to infinite families recently constructed in . Johnson G. Marino O. Polverino R. Trombetti Semifields of order q6 with left nucleus Fq3 and center Fq Finite Fields Appl. 14 2008 and . Ebert G. Marino O. Polverino R. Trombetti Infinite families of new semifields Combinatorica 6 2009 . Then Huang-Johnson semifields of type II and III are extended to new infinite families of semifields of order q6 existing for every prime power q. This work was supported by the Research Project of MIUR Italian Office for University and Research Geometrie su Campi di Galois piani di traslazione e geometrie di incidenza and by the Research
