[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.
)
