In this note we give more easy and short proof of a statement previously proved by P. Kahn that the automorphism group of the discrete Heisenberg group ${ \rm Heis}(3, \mathbb{ Z}) $ is isomorphic to the group $ (\mathbb{ Z} \oplus \mathbb{ Z}) \rtimes GL(2,\mathbb{ Z})$. The method which we suggest to construct this isomorphism gives far more transparent picture of the structure of the automorphism group of the group ${ \rm Heis}(3, \mathbb{ Z}) $.
Categories: math.GR