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

Subject Areas : Group theory

P. Nosratpour ¹

1 - Department of Mathematics, Ilam Branch, Islamic Azad University, Ilam, Iran

Received: 2014-09-01 Accepted : 2014-12-27 Published : 2014-12-01

Keywords: Finite simple group, OD-characterization, group of lie type,

Abstract :

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.

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