GROUPS  OF  MATRICES

(MA1)  Is the group  GL_2(Z[t, t^-1]),  i.e., the group of invertible matrices over the ring of one-variable Laurent polynomials with integral coefficients, generated by elementary and diagonal matrices?

*(MA2) Find a particular matrix from  GL_2(Z[t, t^-1, s, s^-1]),  which is not a product of elementary and diagonal matrices.  Background

(MA3) (a) The subgroup membership problem for the group  SL_3(Z).  Background
(b) The subgroup membership problem for the group  SL_2(Q).

(MA4) (S.Thomas) Does there exist a simple torsion-free linear group?

(MA5) (A.L.Shmelkin) Is it true that identities of any linear group have a finite basis?

(MA6) (Yu. Merzlyakov) Is there a rational number a, |a| < 2, such that two 2x2 matrices   (1, a ; 0, 1)   and   (1, 0 ; a, 1)   generate a free group? Background

(MA7) (L. Vaserstein) For a ring R, let E_n(R) be the subgroup of GL_n(R) generated by elementary matrices. Is there a ring R and an element of E_n(R) (for some n) which is not a commutator?