Geodesic
On alternating subgroup $A_5$ in autotopism group of finite semifield plane
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 47-50.

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We discuss well-known hypothesis that the full collineation group of any finite non-Desarguesian semifield plane is solvable. We continue to investigate the semifield planes of odd order which admit an autotopism subgroup isomorphic to alternating group $A_5$. It is proved that a semifield plane of any odd order does not admit $A_5$ in autotopism group.
Keywords: semifield plane, alternating group.
Mots-clés : autotopism group 
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O. V. Kravtsova. On alternating subgroup $A_5$ in autotopism group of finite semifield plane. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 47-50. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a2/

[1] O.V. Kravtsova, “Semifield planes of even order that admit the Baer involution”, Izv. Irkutsk. Gos. Univ., Ser. Mat., 6:2 (2013), 26-–37 | Zbl

[2] O.V. Kravtsova, “Semifield planes of odd order that admit a subgroup of autotopisms isomorphic to $A_4$”, Russ. Math., 60:9 (2016), 7–22 | DOI | MR | Zbl

[3] O.V. Kravtsova, B.K. Durakov, “A semifield plane of odd order admitting an autotopism subgroup isomorphic to $A_5$”, Sib. Math. J., 59:2 (2018), 309–322 | DOI | MR | Zbl

[4] D.R. Hughes, F.C. Piper, Projective planes, Springer–Verlag, New York–Heidelberg–Berlin, 1973 | MR | Zbl

[5] N.L. Johnson, V. Jha, M. Biliotti, Handbook of finite translation planes, Chapman Hall/CRC, London–New York, 2007 | MR | Zbl

[6] V.D. Mazurov, E.I. Khukhro (eds.), The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed., Sobolev Inst. Math., Novosibirsk, 2006 | MR | Zbl

[7] N.D. Podufalov, O.V. Kravtsova, “On collineation groups of finite semifield projective planes”, Abstracts of talks, International Conference dedicated to the 90th anniversary of the Higher Algebra Department of the Faculty of Mechanics and Mathematics of Moscow State University, 2019, 54