A cylindrical magnetic nanowire system composed of ferromagnetic core and shell layers has been investigated by using effective field theory (EFT) with correlations in the presence of transverse fields and surface shell amorphization. Both weak and strong exchange couplings at the core-shell interface have been considered. The main attention has been focused on the former situation where the system exhibits similar characteristic features with that observed in thin film and semi-infinite systems in which the surface effects are prominent. A complete picture of the phase diagrams and magnetization profiles has been represented and the effect of the surface shell amorphization on these properties has been discussed. Furthermore, we have investigated the ground state behavior of total magnetization m(T) curves and we have observed that m(T) curves exhibit highly non-monotonous and exotic ground states in the presence of frustration in the surface shell. We have also analyzed the necessary conditions for the occurrence of reentrant behavior in the system. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.