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The recognition of finite simple groups with no elements of order $10$ by their element orders | ||
International Journal of Group Theory | ||
دوره 11، شماره 1، خرداد 2022، صفحه 17-22 اصل مقاله (187.35 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.124142.1640 | ||
نویسندگان | ||
Huaiyu He1؛ Wujie Shi* 2 | ||
1Department of Economics and Management, Shanghai University of Political Science and Law, Shanghai 201701, China | ||
2Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160, China3School of Mathe- matics, Suzhou University, Suzhou 215006, China | ||
چکیده | ||
The spectrum of a finite group is the set of its element orders. $H$ is said to be a finite cover of $G$ if $G$ is a homomorphic image of $H$ and $H$ is finite. The main aim of this article is to characterize the finite simple groups with no elements of order 10 by its spectrum among covers. At the same time, above simple groups are completely classified. At last, some results on the recognition by spectrum of above groups are also achieved. | ||
کلیدواژهها | ||
recognition؛ spectrum؛ simple group؛ cover | ||
مراجع | ||
[1] Jianbei An and Wujie Shi, The characterization of finite simple groups with no elements of order six by their element orders, Communications in Algebra, 28 (2000) 3351–3358. [2] R. Brandl and Wujie Shi, Finite groups whose element orders are consecutive integers, J. Algebra, 143 (1991) 388–400.
[3] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of finite groups, Oxford University Press, Eynsham, 1985. [4] L. M.Gordon, Finite simple groups with no elements of order six, Bull. Austral. Math. Soc., 17 (1977) 235–246.
[5] M. A. Grechkoseeva, On element orders in covers of finite simple groups of Lie type, J. Algebra Appl., 14 (2015) 371–384. [6] M. A. Grechkoseeva and Wujie Shi, On finite groups isospectral to finite simple unitary groups over fields of charac- teristic 2, Sib. lektron. Mat. Izv., 10 (2013) 31–37. [7] M. A. Grechkoseeva and M. A. Zvezdina, On recognition of L4 (q) and U4 (q) by spectrum, Siberian Math. J., 61 (2020) 1039–1065. [8] V. D. Mazurov, Recognition of finite groups by a set of orders of their elements, Algebra and Logic, 37 (1998) 371–379.
[9] V. D. Mazurov, Characterizations of Groups by Arithmetic Properties, Algebra Colloq., 11 (2004) 129–140.
[10] V .D. Mazurov, Unrecognizability by spectrum for a finite simple group 3 D4 (2), Algebra and Logic, 52 (2013) 601–605. [11] V. D. Mazurov, Recognition of finite simple groups S4 (q) by their element orders, Algebra Logic, 41 (2002) 93–110.
[12] V. D. Mazurov, Mingchun Xu and Hongping Cao, Recognition of finite simple groups L3 (2m ) and U3 (2m ) by their element orders, Algebra and Logic, 39 (2000) 324–334. [13] N. D. Podufalov, Finite simple groups without elements of orders 6 or 10, Algebra and Logic, 14 (1975) 49–53.
[14] Wujie Shi, A characteristic property of Alt5 , (in Chinese), Southwest-China Normal Univ., 13 (1986) 11–14.
[15] A. V. Vasiliev and M. A. Grechkoseeva, Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2, Algebra and Logic, 47 (2008) 314–320. [16] A. V. Vasiliev, M. A. Grechkoseeva and V. D. Mazurov, Characterization of the finite simple groups by spectrum and order, Algebra and Logic, 81 (2010) 216–218. [17] A. V. Vasiliev and A. M. Staroletov, Almost recognizability by spectrum of simple exceptional groups of Lie type, Algebra and Logic, 53 (2015) 433–449. [18] A. V. Vasiliev and E. P. Vdovin, An adjacency criterion for the prime graph of a finite simple group, Algebra and Logic, 44 (2005) 381–406. [19] J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (1981) 487–513. [20] A. V. Zavarnitsine, Recognition of simple groups U3 (q) by element orders, Algebra and Logic, 45 (2006) 106–116. [21] A. V. Zavarnitsine, Recognition of the simple groups L3 (q) by element orders, J. Group Theory, 7 (2003) 81–97.
[22] K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys., 3 (1892) 265–284. | ||
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