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Algebra i logika, 2015, Volume 54, Number 2, Pages 243–251
DOI: https://doi.org/10.17377/alglog.2015.54.207 (Mi al690) 		 
This article is cited in 15 scientific papers (total in 15 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
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DOI: https://doi.org/10.17377/alglog.2015.54.207
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.
Received: 02.01.2015
English version:
Algebra and Logic, 2015, Volume 54, Issue 2, Pages 161–166
DOI: https://doi.org/10.1007/s10469-015-9335-8
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
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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\paper Infinite groups of finite period
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    • This publication is cited in the following 15 articles:
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    		Алгебра и логика Algebra and Logic
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