On rapid generation of SL2(Fq)
نویسندگان
چکیده
We prove that if A ⊂ Fq\{0} with |A| > Cq 5 6 , then |R(A) ·R(A)| ≥ C′q3, where R(A) = {( a11 a12 a21 a22 ) ∈ SL2(Fq) : a11, a12, a21 ∈ A } . The proof relies on a result, previously established by D. Hart and the author ([3]) which implies that if |A| is much larger than q 3 4 then |{(a11, a12, a21, a22) ∈ A×A×A×A : a11a22 − a12a21 = 1}| = |A|4q−1(1 + o(1)).
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