OD-characterization of almost simple groups related to U3(11)

Subject Areas : History and biography

P. Nosratpour ^{1 *} , M. R. Darafsheh ²

1 - Department of mathematics, Ilam Branch, Islamic Azad university, Ilam, Iran
2 - School of mathematics, College of Science, University of Tehran, Tehran, Iran

Received: 2012-01-01 Accepted : 2012-01-01 Published : 2012-03-01

Keywords: prime graph, recognition, linear group, nite simple group, degree pattern,

Abstract :

Let $L := U_3(11)$. In this article, we classify groups with the same order anddegree pattern as an almost simple group related to $L$. In fact, we prove that $L$, $L:2$ and $L:3$are OD-characterizable, and $L:S_3$ is $5$-fold OD-characterizable.

References:

[1] G. Y. Chen,On structure of Frobenius and 2-Frobenius group, Jornal of Southwest China Normal University, 20(5) (1995), pp. 485-487.(in Chinese)

[2] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford (1985).

[3] D. Gorenstein,Finite Groups, New York, Harpar and Row, (1980).

[4] A. S. Kondratev,Prime graph components of nite simple groups, Math. Sb., 180(6) (1989), pp. 787-797.

[5] M. S. Lucido and A. R. Moghaddamfar,Groups in which all the connected components of their prime graphs are complete, Journal of Group Theory, 7(3) (2004), pp.373-384.

[6] V. D. Mazurov,Recognization of nite groups by a set of orders of their elements, Algebra and Logic, 37(6) (1998), pp.371-379.

[7] A. R. Moghaddamfar, A. R. Zokayi and M. R. Darafsheh,A characterization of nite simple groups by degrees of vertices of their prime graphs, Algebra Colloquium, 12(3) (2005), pp.431-442.

[8] D. S. Passman,Permutation Groups, New York, Benjamin Inc., (1968).

[9] J. S. Williams,Prime graph components of nite groups, J. Alg. 69(2) (1981), pp. 487-513.

[10] A. V. Zavarnitsine,Recognition of alternating groups of degrees r + 1 and r + 2 for prime r and the group of degree 16 by their element order sets, Algebra and Logic, 39(6) (2000), pp. 370-377.

[11] A. V. Zavarnitsine,Finite simple groups with narrow prime spectrum, Siberian Electronic Math. Reports. 6 (2009), pp. 1-12.