Abstract
Let D(m, n; k) be the semi-direct product of two finite cyclic groups \({\mathbb{Z}/m=\langle x\rangle}\) and \({\mathbb{Z}/n=\langle y\rangle}\) , where the action is given by yxy −1 = x k. In particular, this includes the dihedral groups D 2m . We calculate the automorphism group Aut (D(m, n; k)).
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Golasiński, M., Gonçalves, D.L. On automorphisms of split metacyclic groups. manuscripta math. 128, 251–273 (2009). https://doi.org/10.1007/s00229-008-0233-4
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DOI: https://doi.org/10.1007/s00229-008-0233-4