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J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 2, Pages 191–203 (Mi jsfu360)  

This article is cited in 5 scientific papers (total in 5 papers)

Groups with given element orders

Daria V. Lytkinaab, Victor D. Mazurovc

a Siberian State University of Telecommunications and Informtaion Sciencies, Kirova, 86, Novosibirsk, 630102 Russia
b Novosibirsk State University, Pirogova, 2, Novosibirsk, 630090 Russia
c Sobolev Institute of Mathematics, Prospekt Akad. Koptyuga, 4, Novosibirsk, 630090 Russia

Abstract: This paper is a survey of some results and open problems about the structure of (mostly infinite) periodic groups with a given set of element orders. It is based on a talk of authors given on the conference “Algebra and Logic: Theory and Application” dedicated to the 80-th anniversary of V. P. Shunkov (Krasnoyarsk, July 21–27, 2013).

Keywords: spectrum, exponent, periodic group, locally finite group.

Full text: PDF file (202 kB)
References: PDF file   HTML file

UDC: 512.54
Received: 25.12.2013
Received in revised form: 04.02.2014
Accepted: 20.02.2014
Language:

Citation: Daria V. Lytkina, Victor D. Mazurov, “Groups with given element orders”, J. Sib. Fed. Univ. Math. Phys., 7:2 (2014), 191–203

Citation in format AMSBIB
\Bibitem{LytMaz14}
\by Daria~V.~Lytkina, Victor~D.~Mazurov
\paper Groups with given element orders
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 2
\pages 191--203
\mathnet{http://mi.mathnet.ru/jsfu360}


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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. A. S. Mamontov, “The Baer–Suzuki theorem for groups of $2$-exponent $4$”, Algebra and Logic, 53:5 (2014), 422–424  mathnet  crossref  mathscinet  isi
    2. A. S. Mamontov, E. Jabara, “Recognizing $L_3(4)$ by the set of element orders in the class of all groups”, Algebra and Logic, 54:4 (2015), 279–282  mathnet  crossref  crossref  mathscinet  isi
    3. A. S. Mamontov, E. Jabara, “On periodic groups with narrow spectrum”, Siberian Math. J., 57:3 (2016), 538–541  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. W. Guo, A. S. Mamontov, “On groups whose element orders divide $6$ and $7$”, Siberian Math. J., 58:1 (2017), 67–71  mathnet  crossref  crossref  isi  elib  elib
    5. M. Herzog, P. Longobardi, M. Maj, “An exact upper bound for sums of element orders in non-cyclic finite groups”, J. Pure Appl. Algebr., 222:7 (2018), 1628–1642  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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