Expanding phenomena over matrix rings
Journal
Forum Mathematicum
Journal Volume
31
Journal Issue
4
Pages
951-970
Date Issued
2019
Author(s)
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 M2(and | A | ≫ q7/2 then | A( A + A ) | if A is a set of SL2 q and | A | ≫ q5/2 q5/2 , then | A( A + A ) | , | A + A A |A(A+A). We also obtain similar results for the cases of A( B + C ) {A(B+C) and A + BC A+BC , where A , B , C {A,B,C} are sets in M2(q ) M2Fq).
Type
journal article