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This article is cited in 1 scientific paper (total in 1 paper)
Problems on structure for quasifields of orders $16$ and $32$
Vladimir M. Levchuk, Polina K. Shtukkert Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
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, multiplicative loop, orders of elements.
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UDC:
512.554 Received: 10.05.2014 Received in revised form: 10.06.2014 Accepted: 25.06.2014
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Citation:
Vladimir M. Levchuk, Polina K. Shtukkert, “Problems on structure for quasifields of orders $16$ and $32$”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 362–372
Citation in format AMSBIB
\Bibitem{LevSht14}
\by Vladimir~M.~Levchuk, Polina~K.~Shtukkert
\paper Problems on structure for quasifields of orders $16$ and $32$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 3
\pages 362--372
\mathnet{http://mi.mathnet.ru/jsfu382}
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http://mi.mathnet.ru/eng/jsfu382 http://mi.mathnet.ru/eng/jsfu/v7/i3/p362
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This publication is cited in the following articles:
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V. M. Levchuk, P. K. Shtukkert, “Stroenie kvazipolei malykh chetnykh poryadkov”, Tr. IMM UrO RAN, 21, no. 3, 2015, 197–212
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