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Algebra Logika, 2015, Volume 54, Number 2, Pages 243–251 (Mi al690)  

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

Infinite groups of finite period

V. D. Mazurovab, A. Yu. Ol'shanskiic, A. I. Sozutovde

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
c 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA
d Siberian Federal University, pr. Svobodnyi 79, Krasnoyarsk, 660041, Russia
e Reshetnev Siberian State Aerospace University, pr. Gazety Krasnoyarskii Rabochii 31, Krasnoyarsk, 660037, Russia

Abstract: It is proved that there exist periodic groups containing an element of even order and only trivial normal $2$-subgroups in which every pair of involutions generates a $2$-group. This gives a negative answer to Question 11.11a in the Kourovka Notebook. Furthermore, we point out examples of finite simple groups that are recognizable by spectrum in the class of finite groups but not recognizable in the class of all groups.

Keywords: periodic group, periodic product, spectrum of group, recognizability by spectrum, Baire–Suzuki theorem, modular group.

DOI: https://doi.org/10.17377/alglog.2015.54.207

Full text: PDF file (153 kB)
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English version:
Algebra and Logic, 2015, 54:2, 161–166

Bibliographic databases:

UDC: 512.542
Received: 02.01.2015

Citation: V. D. Mazurov, A. Yu. Ol'shanskii, A. I. Sozutov, “Infinite groups of finite period”, Algebra Logika, 54:2 (2015), 243–251; Algebra and Logic, 54:2 (2015), 161–166

Citation in format AMSBIB
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\by V.~D.~Mazurov, A.~Yu.~Ol'shanskii, A.~I.~Sozutov
\paper Infinite groups of finite period
\jour Algebra Logika
\yr 2015
\vol 54
\issue 2
\pages 243--251
\mathnet{http://mi.mathnet.ru/al690}
\crossref{https://doi.org/10.17377/alglog.2015.54.207}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3467213}
\transl
\jour Algebra and Logic
\yr 2015
\vol 54
\issue 2
\pages 161--166
\crossref{https://doi.org/10.1007/s10469-015-9335-8}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84937702773}


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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. I. Sozutov, “Groups with the quasicyclic centralizer of a finite involution”, Siberian Math. J., 57:5 (2016), 881–883  mathnet  crossref  crossref  isi  elib  elib
    2. A. I. Sozutov, “Groups with finite Engel element”, Algebra and Logic, 58:3 (2019), 254–267  mathnet  crossref  crossref  isi
    3. A. I. Sozutov, “Two observations on groups with engel elements”, Siberian Math. J., 60:6 (2019), 1099–1100  mathnet  crossref  crossref  isi  elib
    4. N. V. Maslova, I. N. Belousov, N. A. Minigulov, “Otkrytye problemy, sformulirovannye na XII shkole-konferentsii po teorii grupp, posvyaschennoi 85-letiyu V.A. Belonogova”, Tr. IMM UrO RAN, 26, no. 3, 2020, 275–285  mathnet  crossref  elib
    5. A. S. Mamontov, E. Yabara, “Raspoznavanie $A_7$ po mnozhestvu poryadkov elementov”, Sib. matem. zhurn., 62:1 (2021), 117–130  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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