OD-characterization of $U_3(9)$ and its group of automorphisms

محورهای موضوعی : Group theory

P. Nosratpour ¹ (Department of Mathematics, Ilam Branch, Islamic Azad University, Ilam, Iran)

تاریخ دریافت : 1393/06/10 تاریخ پذیرش : 1393/10/06 تاریخ انتشار : 1393/09/10

کلید واژه: Finite simple group, OD-characterization, group of lie type,

چکیده مقاله :

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)\equivZ_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.

منابع و مأخذ:

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

 

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

 

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

 

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

 

[5] B. Huppert, Endlichen Gruppen I, Springer-Verlag,(1988).

 

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

 

[7] J.S.Williams, Prime graph components of finite groups, J. Alg. 69, No.2,487-513(1981).

 

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