Abstract
We describe {2, 3}-groups in which the order of a product of every two elements of orders at most 4 does not exceed 9 and the centralizer of every involution is a locally cyclic 2-subgroup. In particular, we will prove that these groups are locally finite.
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Lytkina D. V. and Mazurov V. D., “{2, 3}-Groups with no elements of order 6,” Algebra and Logic, 53, No. 6, 463–470 (2014).
GAP—Groups, Algorithms and Programming—a System for Computational Discrete Algebra. Version 4.7.8. 2015.
Mazurov V. D., “On the groups of period 60 with prescribed orders of elements,” Algebra and Logic, 39, No. 3, 189–198 (2000).
Robinson D. J. S., A Course in the Theory of Groups, Springer-Verlag, Berlin; Heidelberg; New York (1982).
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Original Russian Text Copyright © 2016 Jabara E.
Venezia. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 941–954, July–August, 2016; DOI: 10.17377/smzh.2016.57.416. Original article submitted August 17, 2015.
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Jabara, E. On {2, 3}-groups without elements of order 6. Sib Math J 57, 744–746 (2016). https://doi.org/10.1134/S0037446616040169
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DOI: https://doi.org/10.1134/S0037446616040169