Author:
Karabulut Y. Demi̇roğlu,Koh Doowon,Pham Thang,Shen Chun-Yen,Le Anh Vinh
Abstract
Abstract
In this paper, we study expanding phenomena in the setting of matrix rings.
More precisely, we will prove that
•
if A is a set of
{M_{2}(\mathbb{F}_{q})}
and
{\lvert A\rvert\gg q^{7/2}}
, then
{\lvert A(A+A)\rvert,\lvert A+AA\rvert\gg q^{4}}
,
•
if A is a set of
{\mathrm{SL}_{2}(\mathbb{F}_{q})}
and
{\lvert A\rvert\gg q^{5/2}}
, then
{\lvert A(A+A)\rvert,\lvert A+AA\rvert\gg q^{4}}
.
We also obtain similar results for the cases of
{A(B+C)}
and
{A+BC}
, where
{A,B,C}
are sets in
{M_{2}(\mathbb{F}_{q})}
.
Funder
National Research Foundation of Korea
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Ministry of Science and Technology, Taiwan
Subject
Applied Mathematics,General Mathematics
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