I am trying to show thatZ(GL(n,F*)) SL(n,F*)T(n)... This is for any non-zero Field

Where Z is the center of General Linear Group.

andT(n)={a^n=1 | a F*}Im trying to figure this out first

Z(GL(n,F*)) SL(n,F*), since the determinant in this set is suppose to be 1, thendet(aI) = det(a)det(I) = det(a),this has to be 1 to be in the set thereforea=1, which implies this set containsI(n,F*)(The identity matrix) only.

Am I right so far???

Don't really know what else to do.