Discrete Heisenberg group and its automorphism group

Abstract

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 $\mathrm{Heis}(3,\mathbb{Z})$ is isomorphic to the group $(\mathbb{Z}\oplus \mathbb{Z})⋊GL(2,\mathbb{Z})$. The method which we suggest to construct this isomorphism gives far more transparent picture of the structure of the automorphism group of the group $\mathrm{Heis}(3,\mathbb{Z})$.

5 pages, to appear in Mathematical Notes (2015)

References in corpus (1)

• Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields

Cited by in corpus (1)

• Irreducible representations of finitely generated nilpotent groups