ON SUBGROUPS OF GL(2) OVER A CLASS OF NONCOMMUTATIVE RINGS WHICH ARE NORMALIZED BY ELEMENTARY MATRICES

Let R be an associative ring with 1 and Y not-equal R a quasi-ideal of R. Set T2(R, Y) = {diag(u,v)a1,2b2,1C1,2: a+c,b is-an-element-of Y,u, v is-an-element-of GL1R, and v-1au-a, uav-1-a is-an-element-of Y for a ll a is-an-element-of R}. It is proved that if R satisfies 2-fold cond ition, then [E2R,T2(R,Y)] subset-of E2(R,Y) subset-of T2(R,Y); and if R satisfies 6-fold condition, then E2(R,Y) = [E2R,E2(R,Y)] = [E2R,T2(R ,Y)] and the sandwich theorem holds.