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Algebra i logika, 2007, Volume 46, Number 5, Pages 606–626 (Mi al317)  

This article is cited in 12 scientific papers (total in 12 papers)

Periodic groups saturated with $L_3(2^m)$

D. V. Lytkinaa, V. D. Mazurovb

a Siberian Fund for Algebra and Logic
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: Let $\mathfrak M$ be a set of finite groups. A group $G$ is saturated with groups from $\mathfrak M$ if every finite subgroup of $G$ is contained in a subgroup isomorphic to some member of $\mathfrak M$. It is proved that a periodic group $G$ saturated with groups from the set $\{L_3(2^m)\mid m=1,2,\dots\}$ is isomorphic to $L_3(Q)$, for a locally finite field $Q$ of characteristic 2; in particular, it is locally finite.
Keywords: periodic group, locally finite group.
Received: 27.02.2007
English version:
Algebra and Logic, 2007, Volume 46, Issue 5, Pages 330–340
DOI: https://doi.org/10.1007/s10469-007-0033-z
Bibliographic databases:
UDC: 512.544.5
Language: Russian
Citation: D. V. Lytkina, V. D. Mazurov, “Periodic groups saturated with $L_3(2^m)$”, Algebra Logika, 46:5 (2007), 606–626; Algebra and Logic, 46:5 (2007), 330–340
Citation in format AMSBIB
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\jour Algebra Logika
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\pages 606--626
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\pages 330--340
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Linking options:
  • https://www.mathnet.ru/eng/al317
  • https://www.mathnet.ru/eng/al/v46/i5/p606
  • This publication is cited in the following 12 articles:
    1. A. A. Shlepkin, “Gruppy, nasyschennye konechnymi prostymi gruppami $L_3(2^n)$, $L_4(2^l)$”, Tr. IMM UrO RAN, 28, no. 2, 2022, 249–257  mathnet  crossref  mathscinet  elib
    2. A. I. Sozutov, “Groups Saturated with Finite Frobenius Groups”, Math. Notes, 109:2 (2021), 270–279  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. A. Shlepkin, “O periodicheskoi chasti gruppy Shunkova, nasyschennoi lineinymi i unitarnymi gruppami stepeni 3 nad konechnymi polyami chetnoi kharakteristiki”, Tr. IMM UrO RAN, 27, no. 1, 2021, 207–219  mathnet  crossref  elib
    4. A. A. Shlepkin, I. V. Sabodakh, “O dvukh svoistvakh gruppy Shunkova”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 35 (2021), 103–119  mathnet  crossref
    5. A. A. Shlepkin, “O silovskikh 2-podgruppakh grupp Shunkova, nasyschennykh gruppami $L_3(2^m)$”, Tr. IMM UrO RAN, 25, no. 4, 2019, 275–282  mathnet  crossref  elib
    6. D. V. Lytkina, V. D. Mazurov, “Characterization of simple symplectic groups of degree $4$ over locally finite fields of characteristic $2$ in the class of periodic groups”, Siberian Math. J., 58:5 (2017), 850–858  mathnet  crossref  crossref  isi  elib  elib
    7. A. A. Shlepkin, “O periodicheskoi gruppe Shunkova, nasyschennoi konechnymi prostymi gruppami lieva tipa ranga 1”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 16 (2016), 102–116  mathnet
    8. D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami”, Tr. In-ta matem., 23:2 (2015), 72–75  mathnet
    9. 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
    10. A. A. Kuznetsov, K. A. Filippov, “Gruppy, nasyschennye zadannym mnozhestvom grupp”, Sib. elektron. matem. izv., 8 (2011), 230–246  mathnet
    11. D. V. Lytkina, “Groups saturated by finite simple groups”, Algebra and Logic, 48:5 (2009), 357–370  mathnet  crossref  mathscinet  zmath  isi
    12. D. V. Lytkina, L. R. Tukhvatullina, K. A. Filippov, “Periodic groups saturated by finite simple groups $U_3(2^m)$”, Algebra and Logic, 47:3 (2008), 166–175  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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