Geodesic
Groups whose element orders do not exceed~6
Algebra i logika, Tome 53 (2014) no. 5, pp. 570-586.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a periodic group whose element orders do not exceed 6 either is a locally finite or is group of exponent 5.
Keywords: periodic group, locally finite group. 
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D. V. Lytkina; V. D. Mazurov; A. S. Mamontov; E. Jabara. Groups whose element orders do not exceed~6. Algebra i logika, Tome 53 (2014) no. 5, pp. 570-586. http://geodesic.mathdoc.fr/item/AL_2014_53_5_a1/

[1] R. Brandl, W. Shi, “A characterization of finite simple groups with abelian Sylow 2-subgroups”, Ric. Mat., 42:1 (1993), 193–198 | MR | Zbl

[2] Nereshënnye voprosy teorii grupp, Kourovskaya tetrad, 18-e izd., In-t matem. SO RAN, Novosibirsk, 2014 http://www.math.nsc.ru/~alglog/18kt.pdf

[3] W. Burnside, “On an unsettled question in the theory of discontinuous groups”, Q. J. Pure Appl. Math., 33 (1902), 230–238 | Zbl

[4] B. H. Neumann, “Groups whose elements have bounded orders”, J. Lond. Math. Soc., 12 (1937), 195–198 | DOI | MR | Zbl

[5] I. N. Sanov, “Reshenie problemy Bernsaida dlya pokazatelya 4”, Uchen. zap. Leningr. gos. un-ta. Ser. matem., 10, 1940, 166–170 | MR | Zbl

[6] M. Hall (Jr.), “Solution of the Burnside problem for exponent six”, Ill. J. Math., 2 (1958), 764–786 | MR | Zbl

[7] M. F. Newman, “Groups of exponent dividing seventy”, Math. Sci., 4 (1979), 149–157 | MR | Zbl

[8] N. D. Gupta, V. D. Mazurov, “On groups with small orders of elements”, Bull. Aust. Math. Soc., 60:2 (1999), 197–205 | DOI | MR | Zbl

[9] V. D. Mazurov, “O gruppakh perioda 60 s zadannymi poryadkami elementov”, Algebra i logika, 39:3 (2000), 329–346 | MR | Zbl

[10] E. Jabara, “Fixed point free actions of groups of exponent 5”, J. Aust. Math. Soc., 77:3 (2004), 297–304 | DOI | MR | Zbl

[11] V. D. Mazurov, A. S. Mamontov, “O periodicheskikh gruppakh s elementami malykh poryadkov”, Sib. matem. zh., 50:2 (2009), 397–404 | MR

[12] A. S. Mamontov, “Gruppy perioda 12 bez elementov poryadka 12”, Sib. matem. zh., 54:1 (2013), 150–156 | MR | Zbl

[13] The GAP Group, GAP – Groups, Algorithms, Programming – a System for Computational Discrete Algebra, vers. 4.7.5, , 2014 http://www.gap-system.org

[14] P. Hall, G. Higman, “On the $p$-length of $p$-soluble groups and reduction theorems for Burnside's problem”, Proc. Lond. Math. Soc., III Ser., 6:1 (1956), 1–42 | DOI | MR | Zbl

[15] V. P. Shunkov, “O periodicheskikh gruppakh s pochti regulyarnoi involyutsiei”, Algebra i logika, 11:4 (1972), 470–493

[16] M. I. Kargapolov, Yu. I. Merzlyakov, Osnovy teorii grupp, izd. 4-e, pererab. i dopoln., Nauka, Fizmatlit, M., 1996 | MR

[17] D. V. Lytkina, L. R. Tukhvatullina, K. A. Filippov, “O periodicheskikh gruppakh, nasyschennykh konechnym mnozhestvom konechnykh prostykh grupp”, Sib. matem. zh., 49:2 (2008), 394–399 | MR | Zbl

[18] V. D. Mazurov, “Raspoznavanie konechnykh prostykh grupp $S_4(q)$ po poryadkam ikh elementov”, Algebra i logika, 41:2 (2002), 166–198 | MR | Zbl

[19] V. P. Shunkov, “Ob odnom klasse $p$-grupp”, Algebra i logika, 9:4 (1970), 484–496 | MR