Abstract: Let k be a field and G be an algebraic group. If char k=0 Birger Iversen showed in 1976 that the pull-back Br(k)$\to$ Br (G) is an isomorphism if $G$ is simply connected. If fact, he proved this using topological methods for $k$ the field of complex numbers from which the general case follows by Galois cohomology. In my talk I will present one or two (if time permits) algebraic proofs of Iversen's result which show more: If $G$ is simply connected and $k$ arbitrary then the pull-back $n$-torsion Br(k)$\to$ $n$-torsion Br (G) is an isomorphism as long as $n$ is prime to the characteristic of $k$. If $k$ is not perfect of char $p$ I will show then that the pull-back $p$-torsion Br(k)$\to$ $p$-torsion Br(G) is not surjective for any semisimple isotropic connected linear algebraic group over $k$.