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

الموضوعات :

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

تاريخ الإرسال : 06 الإثنين , ذو القعدة, 1435 تاريخ التأكيد : 05 السبت , ربيع الأول, 1436 تاريخ الإصدار : 09 الإثنين , صفر, 1436

الکلمات المفتاحية: Finite simple group, OD-characterization, group of lie type,

ملخص المقالة :

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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