Abstract
Locally finiteness is proved for a group of exponent 36 containing an involution and no elements of order 6.
Similar content being viewed by others
References
Burnside W., “On an unsettled question in the theory of discontinuous groups,” Quart. J. Pure Appl. Math., 33, No. 2, 230–238 (1902).
Neumann B. H., “Groups whose elements have bounded orders,” J. London Math. Soc., 12, 195–198 (1937).
Zhurtov A. Kh. and Mazurov V. D., “Local finiteness of some groups with given element orders,” Vladikavkaz. Mat. Zh., 11, No. 4, 11–15 (2009).
Mazurov V. D., “Groups of exponent 24,” Algebra and Logic, 49, No. 6, 515–525 (2010).
Shunkov V. P., “Periodic groups with an almost regular involution,” Algebra and Logic, 11, No. 4, 260–272 (1972).
Zhurtov A. Kh., “On regular automorphisms of order 3 and Frobenius pairs,” Siberian Math. J., 41, No. 2, 268–275 (2000).
Neumann B. H., “Groups with automorphisms that leave only the neutral element fixed,” Arch. Math., 7, 1–5 (1956).
Sanov I. N., “Solution of Burnside’s problem for n = 4,” Leningrad. Gos. Univ. Uchen. Zap. Ser. Mat. Nauk, 10, No. 55, 166–170 (1940).
Lytkina D. V., “Structure of a group with elements of order at most 4,” Siberian Math. J., 48, No. 2, 283–287 (2007).
Huppert B., Endliche Gruppen. I, Springer-Verlag, Berlin, Heidelberg, and New York (1979).
GAP—Groups, Algorithms and Programming (http://www.gap-system.org).
Author information
Authors and Affiliations
Corresponding author
Additional information
On the occasion of the 70th birthday of Victor Danilovich Mazurov.
Original Russian Text Copyright © 2013 Jabara E. and Lytkina D.V.
The first author was partially supported by the MIUR project “Teoria dei gruppi e applicazioni.” The second author was supported by the Russian Foundation for Basic Research (Grants 11-01-00456, 11-01-91158, and 12-01-90006), the President of the Russian Federation (Grant NSh-4620.2012.1), the Federal Target Program (Contract 14.740.11.0346), and the Integration Project of the Siberian Division of the Russian Academy of Sciences for 2012-2014 (No. 14).
__________
Translated from Sibirskiı Matematicheskiı Zhurnal, Vol. 54, No. 1, pp. 44–48, January–February, 2013.
Rights and permissions
About this article
Cite this article
Jabara, E., Lytkina, D.V. On groups of exponent 36. Sib Math J 54, 29–32 (2013). https://doi.org/10.1134/S0037446613010047
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446613010047