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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 9, Pages 10–25
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This article is cited in 7 scientific papers (total in 7 papers)
Semifield planes of odd order that admit the autotopism subgroup isomorphic to $A_4$
O. V. Kravtsova
Siberian Federal University, 79 Svobodnyi Ave., Krasnoyarsk, 660041 Russia
Abstract:
We evolve an approach to construction and classification of semifield projective planes with the use of the linear space and spread set. We construct the spread set matrix representation for any semifield plane of odd order that admits the Baer involution in translation complement or autotopism subgroup isomorphic to $A_4$. We give the examples of semifield planes of order 81 with the indicated condition.
Keywords:
semifield plane, spread set, Baer involution, isomorphism, autotopism, collineation group, alternating group.
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:9, 7–22
Bibliographic databases:
 
UDC:
519.145
Received: 30.12.2014
Citation:
O. V. Kravtsova, “Semifield planes of odd order that admit the autotopism subgroup isomorphic to $A_4$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 9, 10–25; Russian Math. (Iz. VUZ), 60:9 (2016), 7–22
Citation in format AMSBIB
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\by O.~V.~Kravtsova
\paper Semifield planes of odd order that admit the autotopism subgroup isomorphic to~$A_4$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 9
\pages 10--25
\mathnet{http://mi.mathnet.ru/ivm9148}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 9
\pages 7--22
\crossref{https://doi.org/10.3103/S1066369X16090024}
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Linking options:
http://mi.mathnet.ru/eng/ivm9148 http://mi.mathnet.ru/eng/ivm/y2016/i9/p10
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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O. V. Kravtsova, “On automorphisms of semifields and semifield planes”, Sib. elektron. matem. izv., 13 (2016), 1300–1313
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V. M. Levchuk, O. V. Kravtsova, “Problems on structure of finite quasifields and projective translation planes”, Lobachevskii J. Math., 38:4, SI (2017), 688–698
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O. V. Kravtsova, B. K. Durakov, “A semifield plane of odd order admitting an autotopism subgroup isomorphic to $A_5$”, Siberian Math. J., 59:2 (2018), 309–322
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O. V. Kravtsova, I. V. Sheveleva, “O nekotorykh $3$-primitivnykh polupolevykh ploskostyakh”, Chebyshevskii sb., 20:3 (2019), 316–332
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O. V. Kravtsova, “On alternating subgroup $A_5$ in autotopism group of finite semifield plane”, Sib. elektron. matem. izv., 17 (2020), 47–50
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O. V. Kravtsova, “Polupolevye ploskosti, dopuskayuschie gruppu kvaternionov $Q_8$”, Algebra i logika, 59:1 (2020), 101–115
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O. V. Kravtsova, “Elementary abelian $2$-subgroups in an autotopism group of a semifield projective plane”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 32 (2020), 49–63
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