Automorphisms of Zappa-Szép product fixing a subgroup (Q6193263)

Let \(G\) be a group and \(H, K \leq G\). If \(HK=KH\) (as sets), then \(HK\) is a subgroup of \(G\). If \(G=HK\) and \(H \cap K=1\), then \(G\) is called Zappa-Szép product of \(H\) and \(K\) (introduced by \textit{G. Zappa} in [Atti II. Congr. Un. Mat. Ital. 1940, 119--125 (1940; JFM 68.0037.02)]). In the paper under review, the authors study \(\mathrm{Aut}_{H}(G)\), the automorphism group of the Zappa-Szép product \(G=HK\) fixing the subgroup \(H\). They have computed \(\mathrm{Aut}_{H}(G)\) for a group \(G\) which is the Zappa-Szép product of two cyclic groups \(H\) and \(K\) with \(|H|=p^{2}\) (\(p\) a prime number).