Abstract
It is proved that the simple group 2E6(2) is recognized by its prime graph.
Similar content being viewed by others
References
M. Aschbacher, Finite Group Theory, Cambridge Univ. Press, Cambridge (1986).
R. Carter, Simple Groups of Lie Type, Wiley and Sons, New York (1972).
J. H. Conway, R. Curtis, S. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985).
A. S. Kondrat’ev, “Prime graph components of finite simple groups,” Math. USSR Sb., 67, No. 1, 235–247 (1990).
A. S. Kondrat’ev, “Recognizability of groups E7(2) and E7(3) by prime graph,” Tr. IMM UrO RAN, 20, No. 2, 223–229 (2014).
A. S. Kondrat’ev and V. D. Mazurov, “Recognition of alternating groups of prime degree from the orders of their elements,” Sib. Math. J., 41, No. 2, 294–302 (2000).
V. D. Mazurov, “Characterizations of finite groups by sets of the orders of their elements,” Algebra Logic, 36, No. 1, 23–32 (1997).
V. D. Mazurov, “Groups with a prescribed spectrum,” Izv. Ural. Gos. Univ. Mat. Mekh., No. 7 (36), 119–138 (2005).
I. D. Suprunenko and A. E. Zalesski, “Fixed vectors for elements in modules for algebraic groups,” Intern. J. Algebra Comput., 17, No. 5-6, 1249–1261 (2007).
A. V. Vasil’ev and E. P. Vdovin, “An adjacency criterion in the prime graph of a finite simple group,” Algebra Logic, 44, No. 6, 381–406 (2005).
A. V. Vasil’ev and E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group,” Algebra Logic, 50, No. 4, 291–322 (2011).
J. S. Williams, “Prime graph components of finite groups,” J. Algebra, 69, No. 2, 487–513 (1981).
A. V. Zavarnitsin, “On the recognition of finite groups by the prime graph,” Algebra Logic, 45, No. 4, 220–231 (2006).
A. V. Zavarnitsin, “Finite groups with a five-component prime graph,” Sib. Math. J., 54, No. 1, 40–46 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 115–120, 2019.
Rights and permissions
About this article
Cite this article
Kondrat’ev, A.S. Recognizability by Prime Graph of the Group 2E6(2). J Math Sci 259, 463–466 (2021). https://doi.org/10.1007/s10958-021-05635-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-021-05635-5