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J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 3, Pages 362–372 (Mi jsfu382)  

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.

Full text: PDF file (192 kB)
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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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    This publication is cited in the following articles:
    1. V. M. Levchuk, P. K. Shtukkert, “Stroenie kvazipolei malykh chetnykh poryadkov”, Tr. IMM UrO RAN, 21, no. 3, 2015, 197–212  mathnet  mathscinet  elib
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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