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Licensed Unlicensed Requires Authentication Published by De Gruyter January 8, 2016

On some groups generated by involutions

  • Enrico Jabara EMAIL logo
From the journal Journal of Group Theory

Abstract

Let G be a group generated by the set Γ={gGg2=1g} of its involutions. We prove that if (ab)4=1 for every a,bΓ, then G is a locally finite 2-group. This answers in the affirmative Question 18.58 in the Kourovka notebook ([3]).

References

[1] Baer R., Engelsche Elemente Noetherscher Gruppen, Math. Ann. 133 (1957), 256–270. 10.1007/BF02547953Search in Google Scholar

[2] Lytkina D. V., The structure of a group with elements of order at most 4 (in Russian), Sibirsk. Mat. Zh. 48 (2007), no. 2, 353–358; translation in Sib. Math. J. 48 (2007), no. 2, 283–287. 10.1007/s11202-007-0028-ySearch in Google Scholar

[3] Mazurov V. D. and Khukhro E. I., The Kourovka Notebook. Unsolved Problems in Group Theory. 18th Edition, Institute of Mathematics, Russian Academy of Sciences Siberian Division, Novosibirsk, 2014. Search in Google Scholar

[4] Razmyslov J. P., The Hall–Higman problem (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), no. 4, 833–847. 10.1070/IM1979v013n01ABEH002015Search in Google Scholar

[5] Sanov I. N., Solution of Burnside’s problem for exponent 4 (in Russian), Leningrad State Univ. Ann. Math. Ser. 10 (1940), 166–170. Search in Google Scholar

[6] The GAP Group , GAP – Groups, Algorithms,Programming, Version 4.7.8, 2015, http://www.gap-system.org. Search in Google Scholar

Received: 2015-10-22
Revised: 2015-11-29
Published Online: 2016-1-8
Published in Print: 2016-7-1

© 2016 by De Gruyter

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