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The discrete Heisenberg group and its automorphism group. (English. Russian original) Zbl 1332.22013
Math. Notes 98, No. 1, 185-188 (2015); translation from Mat. Zametki 98, No. 1, 152-155 (2015).
In [“Automorphisms of the discrete Heisenberg groups”, Preprint , http://www.math.cornell.edu/m/People/Faculty/kahn], P. Kahn showed that the automorphism group of the discrete Heisenberg group \(\mathrm{Heis}(3,\mathbb{Z})\) is isomorphic to the group \((\mathbb{Z} \oplus \mathbb{Z}) \rtimes \mathrm{GL}(2,\mathbb{Z})\). In the paper under review, the author gives a simpler and shorter proof of this result.

MSC:
22E40 Discrete subgroups of Lie groups
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References:
[1] P. Kahn, Automorphisms of the Discrete Heisenberg Groups, Preprint (2005), http://www.math. cornell.edu/m/People/Faculty/kahn.
[2] D. V. Osipov and A. N. Parshin, Trudy Mat. Inst. Steklov 292 (2016) [Proc. Steklov Inst. Math. 292 (2016)] (to appear).
[3] C. Kassel and V. Turaev, Braid Groups, in Grad. Texts inMath. (Springer, New-York, 2008), Vol. 247.
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