Geodesic
Problems on structure for quasifields of orders $16$ and $32$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 362-372

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Well-known method of the construction of finite projective translation planes (analogously, semifield planes) uses their correspondence with quasifields (resp., semifields). We distinguish certain questions on the structure of any finite quasifield (possible maximal subfields, the property of cyclicity of multiplicative loop of non-zero elements and possible orders of elements). In the present paper we discover some anomalous properties of finite quasifields of small even orders.
Keywords: projective translation plane, quasifield, semifield, orders of elements.
Mots-clés : multiplicative loop 
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Vladimir M. Levchuk; Polina K. Shtukkert. Problems on structure for quasifields of orders $16$ and $32$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 3, pp. 362-372. http://geodesic.mathdoc.fr/item/JSFU_2014_7_3_a10/