For citation: Mazurov V. D. Unrecognizable by spectrum finite simple groups and their isospectral groups. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol.17, no. 2, pp.47-55.
DOI 10.23671/VNC.2015.2.7280
1. Shi W. J. A characteristic property of the Mathieu groups.
Chinese Ann. Math. Ser. A, 1988, vol. 9, no. 5, pp. 575-580
(Chinese).
2. Chigira N., Shi W. J. More on the set of element orders in
finite groups. Northeast. Math. J., 1996, vol. 12, no. 3, pp.
257-260.
3. Mazurov V. D. Raspoznavanie konechnyh neprostyh grupp po
mnozhestvu porjadkov ih jelementov. Algebra i Logika [Algebra and
Logic], 1997, vol. 36, no. 3, pp. 304-322 (Russian).
4. Mazurov V. D., Shi V. Dzh. A criterion of unrecognizability by
spectrum for finite groups. Algebra and Logic [Algebra i Logika],
2012, vol. 51, no. 2, pp. 160-162.
5. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson
R. A. Atlas of Finite Groups, Oxford, Clarendon Press, 1985.
6. Brandl R., Shi W. J. Finite groups whose element orders are
cosecutive integers. J. Algebra, 1991, vol. 143, no. 2, pp. 388-400.
7. Lytkin Yu. V. On groups critical with respect to a set of
natural numbers. Sib. Elektron. Mat. Izv., 2013, vol. 10, pp.
666-675.
8. Mazurov V. D. Raspoznavanie konechnyh grupp po mnozhestvu
porjadkov ih jelementov. Algebra i Logika [Algebra and Logic], 1998,
vol. 37, no. 6, pp. 651-666 (Russian).
9. Staroletov A. M. Groups isospectral to the degree 10 alternating
group. Siberian Math. J. [Sibirsk. Mat. Zh.], 2010, vol. 51,
no. 3, pp. 507-514.
10. Lytkin Ju. V. Groups critical with respect to the spectra of
alternating and sporadic groups. Siberian Math. J. [Sibirsk. Mat.
Zh.], 2015, vol. 56, no. 1, pp.101-106.
11. Zavarnitsine A. V. Exceptional action of the simple groups
L_4(q) in the defining characteristic. Sib. Elektron. Mat. Izv.,
2008, vol. 5, pp. 68-74.
12. Mazurov V. D. Recognition of finite simple groups S_4(q) by
their element orders. Algebra and Logic[Algebra i Logika],
2002, vol. 41, no. 2, pp 93-110.
13. Wilson R. et. al. Atlas of finite group representations [URL:
http://brauer.maths.qmul.ac.uk/ Atlas/v3/].
14. Aleeva M. R. On finite simple groups with the Set of element
orders as in a frobenius group or a double frobenius group. Math.
Notes [Mat. Zametki], 2003, vol. 73, no. 3, pp. 299-313.
15. Zavarnicin A. V. A solvable group isospectral to S_4(3).
Siberian Math. J. [Sibirsk. Mat. Zh.], 2010, vol. 51, no. 1, pp. 20-24.
16. Jansen C., Lux K., Parker R., Wilson R. An Atlas of Brauer
Characters, Oxford, Clarendon Press, 1995.
17. Grechkoseeva M. A. On element orders in covers of finite
simple classical groups. J. Algebra, 2011, vol. 339, pp. 304-319.
18. Mazurov V. D., Su M. Ch., Chao Ch. P. Recognition of finite
simple groups L_3(2^m ) ANDU_3(2^m ) by their element orders.
Algebra and Logic [Algebra i Logika], 2000, vol. 39,
no. 5, pp. 324-334.
19. Grechkoseeva M. A., Staroletov A. M. Unrecognizability by
spectrum of finite simple orthogonal groups of dimension nine. Sib.
Elektron. Mat. Izv., 2014, vol. 11, pp. 921-928.
20. Mazurov V. D., Moghaddamfar A. R. The recognition of the simple
group S_8(2) by its spectrum. Algebra Colloquium, 2006, vol. 3, no.
4, pp. 643-646.
21. Mazurov V. D. Unrecognizability by spectrum for a finite simple
group ^3_D 4(2). Algebra and Logic [Algebra i Logika], 2013,
vol. 52, no. 5, pp. 400-403.
22. Praeger C. E., Shi W. J. A characterization of some alternating
and symmetric groups. Commun. Algebra, 1994, vol. 22, no. 5, pp.
1507-1530.
23. Mazurov V. D., Shi W. J. A note to the characterization of
sporadic simple groups. Algebra Colloquium, 1998, vol. 5, no. 3, pp.
285-288.