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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 9, Pages 10–25 (Mi ivm9148)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04897
16-01-00707


Full text: PDF file (254 kB)
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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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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84979210850}


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    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:
    1. O. V. Kravtsova, “On automorphisms of semifields and semifield planes”, Sib. elektron. matem. izv., 13 (2016), 1300–1313  mathnet  crossref
    2. 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  crossref  mathscinet  zmath  isi  scopus
    3. 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  mathnet  crossref  crossref  isi  elib
    4. O. V. Kravtsova, I. V. Sheveleva, “O nekotorykh $3$-primitivnykh polupolevykh ploskostyakh”, Chebyshevskii sb., 20:3 (2019), 316–332  mathnet  crossref
    5. O. V. Kravtsova, “On alternating subgroup $A_5$ in autotopism group of finite semifield plane”, Sib. elektron. matem. izv., 17 (2020), 47–50  mathnet  crossref
    6. O. V. Kravtsova, “Polupolevye ploskosti, dopuskayuschie gruppu kvaternionov $Q_8$”, Algebra i logika, 59:1 (2020), 101–115  mathnet  crossref
    7. 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  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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