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Sib. Èlektron. Mat. Izv., 2007, Volume 4, Pages 345–360 (Mi semr162)  

This article is cited in 10 scientific papers (total in 10 papers)

Research papers

Regular orbits of solvable linear $p'$-groups

E. P. Vdovin

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: In this paper we prove that a solvable linear $p'$-group $G\le GL(V)$, where $p$ is the characteristic of the underlying field of $V$, has a regular orbit on $V\times V$.

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Document Type: Article
UDC: 512.5
MSC: 20D10, 20D20
Received August 23, 2007, published September 7, 2007
Language: English

Citation: E. P. Vdovin, “Regular orbits of solvable linear $p'$-groups”, Sib. Èlektron. Mat. Izv., 4 (2007), 345–360

Citation in format AMSBIB
\Bibitem{Vdo07}
\by E.~P.~Vdovin
\paper Regular orbits of solvable linear $p'$-groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 345--360
\mathnet{http://mi.mathnet.ru/semr162}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2465432}
\zmath{https://zbmath.org/?q=an:1134.20058}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Zenkov, “On intersections of solvable Hall subgroups in finite nonsolvable groups”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S250–S253  mathnet  crossref  elib
    2. E. P. Vdovin, V. I. Zenkov, “On the intersections of solvable Hall subgroups in finite groups”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S234–S243  mathnet  crossref  isi  elib
    3. E. P. Vdovin, D. O. Revin, “Theorems of Sylow type”, Russian Math. Surveys, 66:5 (2011), 829–870  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Vdovin E.P., “On the Base Size of a Transitive Group with Solvable Point Stabilizer”, J. Algebra. Appl., 11:1 (2012), 1250015  crossref  mathscinet  mathscinet  zmath  isi  elib
    5. E. P. Vdovin, “On intersection of solvable Hall subgroups in finite simple exceptional groups of Lie type”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S183–S190  mathnet  crossref  mathscinet  isi  elib
    6. S. F. Kamornikov, “One characterization of the Gaschütz subgroup of a finite soluble group”, J. Math. Sci., 233:1 (2018), 42–49  mathnet  crossref
    7. Halasi Z., Podoski K., “Every Coprime Linear Group Admits a Base of Size Two”, Trans. Am. Math. Soc., 368:8 (2016), 5857–5887  crossref  mathscinet  zmath  isi
    8. Chen X., Cossey J.P., Lewis M.L., Tong-Viet H.P., “Blocks of Small Defect in Alternating Groups and Squares of Brauer Character Degrees”, J. Group Theory, 20:6 (2017), 1155–1173  crossref  mathscinet  zmath  isi  scopus
    9. Kamornikov S., “Intersections of Prefrattini Subgroups in Finite Soluble Groups”, Int. J. Group Theory, 6:2 (2017), 1–5  crossref  mathscinet  isi
    10. S. Ii, S. F. Kamornikov, L. Syao, “O kharakterizatsii yadra $\pi$-prefrattinievoi podgruppy konechnoi razreshimoi gruppy”, Sib. matem. zhurn., 60:1 (2019), 74–81  mathnet  crossref
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