Is there any way to compute $Aut(H \rtimes K)$? I don't know either how to compute the simplest ones, like semidirect product of two cyclic groups. Any hint, books to read or articles about this theme? Thanks in advance.
2026-03-30 03:20:21.1774840821
Automorphisms of a semidirect product.
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I don't think there is any general pattern to such a computation.
For example, direct products are a special case of semidirect products. So, just to have a concrete example, any general method would have to deal with the unexpected complexities of $$Aut(\mathbb{Z}^3 \times \mathbb{Z}^7) = Aut(\mathbb{Z}^{10}) = GL(10,\mathbb{Z}) $$