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

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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. Lytkina^ab, Victor D. Mazurov^c

^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.

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

Журнал Сибирского федерального университета. Серия "Математика и физика"

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