Algebra i logika
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Algebra Logika:

Personal entry:
Save password
Forgotten password?

Algebra Logika, 2008, Volume 47, Number 3, Pages 288–306 (Mi al360)  

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

Periodic groups saturated by finite simple groups $U_3(2^m)$

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

a Siberian Fund for Algebra and Logic
b Krasnoyarsk State Agricultural University

Abstract: Let $\mathfrak M$ be a set of finite groups. A group $G$ is said to be saturated by the groups in $\mathfrak M$ if every finite subgroup of $G$ is contained in a subgroup isomorphic to a member of $\mathfrak M$. It is proved that a periodic group $G$ saturated by groups in a set $\{U_3(2^m)\mid m=1,2,…\}$ is isomorphic to $U_3(Q)$ for some locally finite field $Q$ of characteristic 2; in particular, $G$ is locally finite.

Keywords: periodic group, finite group, saturated group.

Full text: PDF file (241 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2008, 47:3, 166–175

Bibliographic databases:

UDC: 512.542.5
Received: 11.02.2008

Citation: D. V. Lytkina, L. R. Tukhvatullina, K. A. Filippov, “Periodic groups saturated by finite simple groups $U_3(2^m)$”, Algebra Logika, 47:3 (2008), 288–306; Algebra and Logic, 47:3 (2008), 166–175

Citation in format AMSBIB
\by D.~V.~Lytkina, L.~R.~Tukhvatullina, K.~A.~Filippov
\paper Periodic groups saturated by finite simple groups~$U_3(2^m)$
\jour Algebra Logika
\yr 2008
\vol 47
\issue 3
\pages 288--306
\jour Algebra and Logic
\yr 2008
\vol 47
\issue 3
\pages 166--175

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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, “Groups saturated by finite simple groups”, Algebra and Logic, 48:5 (2009), 357–370  mathnet  crossref  mathscinet  zmath  isi
    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. D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami”, Tr. In-ta matem., 23:2 (2015), 72–75  mathnet
    5. 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
    6. 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
    7. 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
    8. 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
    9. D. V. Lytkina, V. D. Mazurov, “Periodicheskie gruppy, nasyschennye konechnymi prostymi gruppami lieva tipa $B_3$”, Sib. matem. zhurn., 61:3 (2020), 634–640  mathnet  crossref
    10. A. I. Sozutov, “On groups with a strongly embedded unitary subgroup”, Sib. elektron. matem. izv., 17 (2020), 1128–1136  mathnet  crossref
    11. 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
    12. A. A. Shlepkin, I. V. Sabodakh, “O dvukh svoistvakh gruppy Shunkova”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 35 (2021), 103–119  mathnet  crossref
  • Алгебра и логика Algebra and Logic
    Number of views:
    This page:352
    Full text:107
    First page:3

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022