Abstract
We prove that a group with the not maximal quasicyclic centralizer of a finite involution is locally finite.
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References
Adian S. I., The Burnside Problem and Identities in Groups, Springer-Verlag, Berlin and New York (1978).
Sozutov A. I. and Durakov E. B., “Two questions in The Kourovka Notebook,” Algebra and Logic, 52, No. 5, 422–425 (2013).
Mazurov V. D., Ol’shanskiĭ A. Yu., and Sozutov A. I., “Infinite groups of finite period,” Algebra and Logic, 54, No. 2, 161–166 (2015).
Mazurov V. D., “Infinite groups with Abelian centralizers of involutions,” Algebra and Logic, 39, No. 1, 42–49 (2000).
Sozutov A. I., “Some infinite groups with strongly embedded subgroup,” Algebra and Logic, 39, No. 5, 345–353 (2000).
Sozutov A. I. and Suchkov N. M., “On infinite groups with a given strongly isolated 2-subgroup,” Math. Notes, 68, No. 2, 237–247 (2000).
Suchkov N. M., “On periodic groups with Abelian centralizers of involution,” Sb. Math., 193, No. 2, 303–310 (2002).
Mazurov V. D. and Khukhro E. I. (Eds.), The Kourovka Notebook: Unsolved Problems in Group Theory, 15th ed., Sobolev Inst. Math., Novosibirsk (2002).
Sozutov A. I., Suchkov N. M., and Suchkova N. G., Infinite Groups with Involutions, Sib. Fed. Univ., Krasnoyarsk (2011).
Belyaev V. V., “Groups with an almost-regular involution,” Algebra and Logic, 26, No. 5, 315–317 (1987).
Sozutov A. I., “Groups with an almost regular involution,” Algebra and Logic, 46, No. 3, 195–199 (2007).
Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1979).
Ito N., “Über das Product von zwei abelschen Gruppen,” Math. Z., Bd 62, Heft 4, 400–401 (1955).
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The author was supported by the Russian Foundation for Basic Research (Grant 15–01–04897-a).
Krasnoyarsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 11127–1130, September–October, 2016; DOI: 10.17377/smzh.2016.57.518.
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Sozutov, A.I. Groups with the quasicyclic centralizer of a finite involution. Sib Math J 57, 881–883 (2016). https://doi.org/10.1134/S0037446616050189
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DOI: https://doi.org/10.1134/S0037446616050189