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Sibirsk. Mat. Zh., 2008, Volume 49, Number 2, Pages 394–399 (Mi smj1848)  

This article is cited in 19 scientific papers (total in 19 papers)

The periodic groups saturated by finitely many finite simple groups

D. V. Lytkinaa, L. R. Tukhvatullinab, K. A. Filippovb

a Novosibirsk State University
b Krasnoyarsk State Agricultural University

Abstract: Denote by $\mathfrak M$ the set whose elements are the simple 3-dimensional unitary groups $U_3(q)$ and the linear groups $L_3(q)$ over finite fields. We prove that every periodic group, saturated by the groups of a finite subset of $\mathfrak M$, is finite.

Keywords: saturation of a group by a set of groups, periodic group.

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English version:
Siberian Mathematical Journal, 2008, 49:2, 317–321

Bibliographic databases:

UDC: 512.54
Received: 15.11.2007

Citation: D. V. Lytkina, L. R. Tukhvatullina, K. A. Filippov, “The periodic groups saturated by finitely many finite simple groups”, Sibirsk. Mat. Zh., 49:2 (2008), 394–399; Siberian Math. J., 49:2 (2008), 317–321

Citation in format AMSBIB
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\paper The periodic groups saturated by finitely many finite simple groups
\jour Sibirsk. Mat. Zh.
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\vol 49
\issue 2
\pages 394--399
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\transl
\jour Siberian Math. J.
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\vol 49
\issue 2
\pages 317--321
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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. D. V. Lytkina, “Periodic groups acting freely on Abelian groups”, Algebra and Logic, 49:3 (2010), 256–261  mathnet  crossref  mathscinet  zmath
    2. D. V. Lytkina, “On the periodic groups saturated by direct products of finite simple groups”, Siberian Math. J., 52:2 (2011), 267–273  mathnet  crossref  mathscinet  isi
    3. A. A. Kuznetsov, K. A. Filippov, “Gruppy, nasyschennye zadannym mnozhestvom grupp”, Sib. elektron. matem. izv., 8 (2011), 230–246  mathnet
    4. Filippov K.A., “O periodicheskikh gruppakh shunkova, nasyschennykh prostymi trekhmernymi unitarnymi gruppami”, Vestnik sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva, 2012, no. 2, 78–80  elib
    5. I. V. Sabodakh, “O periodicheskikh gruppakh, nasyschennykh konechnym mnozhestvom grupp”, Sib. elektron. matem. izv., 11 (2014), 321–326  mathnet
    6. D. V. Lytkina, V. D. Mazurov, A. S. Mamontov, E. Jabara, “Groups whose element orders do not exceed 6”, Algebra and Logic, 53:5 (2014), 365–376  mathnet  crossref  mathscinet  isi
    7. Jabara E. Lytkina D. Mamontov A., “Recognizing M-10 By Spectrum in the Class of All Groups”, Int. J. Algebr. Comput., 24:2 (2014), 113–119  crossref  mathscinet  zmath  isi  elib  scopus
    8. A. A. Shlepkin, “On the periodic groups saturated with projective linear groups”, Siberian Math. J., 56:4 (2015), 761–764  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami”, Tr. In-ta matem., 23:2 (2015), 72–75  mathnet
    10. A. A. Shlepkin, “Gruppy Shunkova, nasyschennye lineinymi i unitarnymi gruppami stepeni 3 nad polyami nechetnykh poryadkov”, Sib. elektron. matem. izv., 13 (2016), 341–351  mathnet  crossref
    11. D. V. Lytkina, V. D. Mazurov, “On $2$-groups with finite subgroups of rank $2$”, Siberian Math. J., 57:3 (2016), 532–537  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. A. A. Shlepkin, “O periodicheskikh gruppakh i gruppakh Shunkova, nasyschennykh unitarnymi gruppami stepeni tri”, Tr. IMM UrO RAN, 22, no. 3, 2016, 299–307  mathnet  crossref  mathscinet  elib
    13. D. V. Lytkina, A. A. Shlepkin, “Periodic groups saturated with finite simple groups of types $U_3$ and $L_3$”, Algebra and Logic, 55:4 (2016), 289–294  mathnet  crossref  crossref  isi
    14. A. A. Shlepkin, “Periodic groups saturated with finite simple groups of Lie type of rank $1$”, Algebra and Logic, 57:1 (2018), 81–86  mathnet  crossref  crossref  isi
    15. A. A. Shlepkin, “O gruppakh Shunkova, nasyschennykh konechnymi prostymi gruppami”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 24 (2018), 51–67  mathnet  crossref
    16. D. V. Lytkina, A. A. Shlepkin, “Periodic groups saturated with the linear groups of degree $2$ and the unitary groups of degree $3$ over finite fields of odd characteristic”, Siberian Adv. Math., 28:3 (2018), 175–186  mathnet  crossref  crossref  elib
    17. A. A. Shlepkin, “O periodicheskoi chasti gruppy Shunkova, nasyschennoi spletennymi gruppami”, Tr. IMM UrO RAN, 24, no. 3, 2018, 281–285  mathnet  crossref  elib
    18. D. V. Lytkina, A. I. Sozutov, A. A. Shlepkin, “Periodicheskie gruppy 2-ranga dva, nasyschennye konechnymi prostymi gruppami”, Sib. elektron. matem. izv., 15 (2018), 786–796  mathnet  crossref
    19. D. V. Lytkina, V. D. Mazurov, “Characterization of simple symplectic groups of degree 4 over locally finite fields in the class of periodic groups”, Algebra and Logic, 57:3 (2018), 201–210  mathnet  crossref  crossref  isi
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