In the book "Structure of Groups of Prime Power order (Charles Richard Leedham-Green, Susan McKay), there is an exercise (2.1.10), which asks to show that the automorphism group of ($\mathbb{Z}_p \times \mathbb{Z}_p) \rtimes \mathbb{Z}_p$ is ($\mathbb{Z}_p \times \mathbb{Z}_p) \rtimes GL(2,p)$. To prove this, first, it is easy to show that there is a short exact sequence $1 \rightarrow \mathbb{Z}_p \times \mathbb{Z}_p \rightarrow Aut((\mathbb{Z}_p \times \mathbb{Z}_p) \rtimes \mathbb{Z}_p) \rightarrow GL(2,p) \rightarrow 1$. Therefore it remains to show that "this exact sequence is split". How to show it?
Automorphisms of a non-abelian group of order $p^{3}$
6
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group-theory
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0@Rahul: Could you typeset your question and title? – 2011-01-28