Voir la notice de l'article provenant de la source Math-Net.Ru
@article{TIMB_2010_18_1_a7, author = {V. D. Mazurov}, title = {Periodic groups with prescribed element orders}, journal = {Trudy Instituta matematiki}, pages = {72--78}, publisher = {mathdoc}, volume = {18}, number = {1}, year = {2010}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a7/} }
V. D. Mazurov. Periodic groups with prescribed element orders. Trudy Instituta matematiki, Tome 18 (2010) no. 1, pp. 72-78. http://geodesic.mathdoc.fr/item/TIMB_2010_18_1_a7/
[1] F. Levi, B.L. van der Waerden, “Über eine besondere Klasse von Gruppen”, Abh. Math. Semin. Hamburg Univ., 9 (1932), 154–158. | DOI | Zbl
[2] F.V. Levi, “Groups in which the commutator operations satisfy certain algebraical conditions”, J. Indian Math. Soc., 6 (1942), 87–97 | MR | Zbl
[3] I.N. Sanov, “Solution of the Burnside problem for exponent 4 (in Russian)”, Uchenye zap. Leningr. gos. universiteta, matem. seriya, 10 (1940), 166–170 | MR
[4] Yu.P. Razmyslov, “The Hall-Higman problem”, Izv. AN SSSR. Ser. matem., 42:4 (1978), 833–847 (in Russian) | MR | Zbl
[5] M. Hall Jr., “Solution of the Burnside problem for exponent six”, Illinois J. Math., 2 (1958), 764–786 | MR | Zbl
[6] S.I. Adyan, The Burnside problem and identities in groups, Nauka, Moscow, 1975 (in Russian) | MR | Zbl
[7] A.Yu. Ol'shanskii, The geometry of defining relations in groups, Nauka, Moscow, 1989 (in Russian) | MR
[8] S.V. Ivanov, “The free Burnside groups of sufficiently large exponents”, Internat. J. Algebra Comput., 4 (1994), 3–308 | DOI | MR
[9] I.G. Lysenok, “Infinite Burnside groups of even exponents”, Izv. RAN. Ser. matem., 60:3 (1996), 3–224 (in Russian) | MR | Zbl
[10] B.H. Neumann, “Groups whose elements have bounded orders”, J. London Math. Soc., 12 (1937), 195–198 | DOI
[11] D.D. Lytkina, “The structure of a group whose element orders are at most 4”, Sib. matem. zhurn., 48:2 (2007), 353–358 (in Russian) | MR | Zbl
[12] E. Jabara., “Fixed point free action of groups of exponent 5”, J. Austral. Math. Soc., 77 (2004), 297–304 | DOI | MR | Zbl
[13] M.F. Newman, “Groups of exponent dividing seventy”, Math. Scientist., 4 (1979), 149–157 | MR | Zbl
[14] A.Kh. Zhurtov, V.D. Mazurov, “On recognizing finite simple groups $L_2(2^m)$ in the class of all groups”, Sib. matem. zhurn., 40:1 (1999), 75–78 (in Russian) | MR | Zbl
[15] V.D. Mazurov, “On infinite groups with abelian centralizers of involutions”, Algebra i logika, 39:1 (2000), 74–86 (in Russian) | MR | Zbl
[16] A.I. Sozutov, “On the structure of the noninvariant multiplier in certain Frobenius groups”, Sib. matem. zhurn., 35:4 (1994), 893–901 (in Russian) | MR | Zbl
[17] N.D. Gupta, V.D. Mazurov, “On groups with small orders of elements”, Bull. Austral. Math. Soc., 60 (1999), 197–205 | DOI | MR | Zbl
[18] V.D. Mazurov, “On groups of exponent 60 with prescribed orders of elements”, Algebra i logika, 39:3 (2000), 329–346 (in Russian) | MR | Zbl
[19] A.Kh. Zhurtov, “On regular automorphisms of order 3 and Frobenius pairs”, Sib. matem. zhurn., 41:2 (2000), 329–338 (in Russian) | DOI | MR | Zbl
[20] A.Kh. Zhurtov, “On quadratic automorphisms of abelian groups”, Algebra i logika, 39:3 (2000), 320–328 (in Russian) | MR | Zbl
[21] V.D. Mazurov, A.S. Mamontov, “On periodical groups with elements of small orders”, Sib. matem. zhurn., 50:2 (2009), 397–404 (in Russian) | MR
[22] D.V. Lytkina, A.A. Kuznetsov, “Recognizability by spectrum of the group $L_2(7)$ in the class of all groups”, Siberian Electronic Mathematical Reports, 4 (2007), 136–140 | MR | Zbl
[23] D. Sonkin, On groups of large exponents $n$ and $n$-periodic products, PhD Thesis, Vandebilt Univ., Nashville, Tennessee, 2005 | MR
[24] Shi W., “A new characterization of the sporadic simple groups”, Group Theory, Proc. 1987 Singapore Group Theory Conference, Walter de Gruyter, Berlin–New York, 1989, 531–540 | MR
[25] Bi J. and Shi W., “A characteristic property for each finite projective special linear group”, Lecture Notes in Math., 1456, Springer–Verlag, Berlin, 1990, 171–180 | MR
[26] Bi J. and Shi W., “A characterization of Suzuki-Ree groups”, Science in China (Ser. A), 34:1 (1991), 14–19 | MR | Zbl
[27] Bi J. and Shi W., “A new characterization of the alternating groups”, Southeast Asian Bull. Math., 16:1 (1992), 81–90 | MR | Zbl
[28] Shi W., “The pure quantitative characterization of finite simple groups (I)”, Progress in Natural Science, 4:3 (1994), 316–326 | MR
[29] Cao H. and Shi W., “The pure quantitative characterization of finite projective special unitary groups”, Science in China (Ser. A), 45:6 (2002), 761–772 | MR | Zbl
[30] Shi W. and Xu M., “Pure quantitative characterization of finite simple groups $^2D_n(q)$ and $D_l(q)$ ($l$ odd)”, Algebra Colloq., 10:3 (2003), 427–443 | MR | Zbl
[31] Williams J.S., “Prime graph components of finite groups”, J. Algebra, 69:2 (1981), 487–513 | DOI | MR | Zbl
[32] Kondrat'ev A.S., “On prime graph components of finite simple groups”, Math. USSR-Sb., 67:1 (1990), 235–247 | DOI | MR
[33] Vasil'ev A.V., “On connection between the structure of a finite group and properties of its prime graph”, Siberian Math. J., 46:3 (2005), 396–404 | DOI | MR
[34] Vasiliev A.V. and Vdovin E.P., “An adjacency criterion for the prime graph of a finite simple group”, Algebra and Logic, 44:6 (2005), 381–406 | DOI | MR | Zbl
[35] Mazurov V.D., “Recognition of finite simple groups $S_4(q)$ by their element orders”, Algebra and Logic, 41:2 (2002), 93–110 | DOI | MR | Zbl
[36] Vasil'ev A.V. and Grechkoseeva M.A., “On recognition by spectrum of finite simple linear groups over fields of characteristic 2”, Siberian Math. J., 46:4 (2005), 593–600 | DOI | MR
[37] Vasilyev A.V. and Grechkoseeva M.A., “Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2”, Algebra and Logic, 47:5 (2008), 314–320 | DOI | MR