|
This article is cited in 6 scientific papers (total in 6 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}
Linking options:
http://mi.mathnet.ru/eng/jsfu360 http://mi.mathnet.ru/eng/jsfu/v7/i2/p191
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:
-
A. S. Mamontov, “The Baer–Suzuki theorem for groups of $2$-exponent $4$”, Algebra and Logic, 53:5 (2014), 422–424
-
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
-
A. S. Mamontov, E. Jabara, “On periodic groups with narrow spectrum”, Siberian Math. J., 57:3 (2016), 538–541
-
W. Guo, A. S. Mamontov, “On groups whose element orders divide $6$ and $7$”, Siberian Math. J., 58:1 (2017), 67–71
-
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
-
A. S. Mamontov, “O periodicheskikh gruppakh, izospektralnykh $A_7$”, Sib. matem. zhurn., 61:1 (2020), 137–147
|
Number of views: |
This page: | 487 | Full text: | 151 | References: | 34 |
|