Group communication, security and 5G technology present a unique dimension of challenges and security remains crucial in the successful deployment of 5G technology across different industry. Group key management plays a vital role in secure group communication. This research work studies various group key management schemes for mobile wireless technology and then a new scheme is proposed and evaluated. The main architecture is analysed, while the components and their roles are established, trust and keying relationships are evaluated, as well as detailed functional requirements. A detailed description of the main protocols required within the scheme is also described. A numerical and simulation analysis is employed to assess the proposed scheme with regards to fulfilling the security requirement and performance requirements. The impact of group size variation, the impact of mobility rate variation are studied with regards to the average rekeying messages induced by each event and 1-affects-n phenomenon. The results obtained from the simulation experiments show that the proposed scheme outperformed other solutions with a minimal number of rekeying messages sent and less number of affected members on each event. The security requirements demonstrate that backward and forward secrecy is preserved and maintained during mobility between areas. Finally, the research work also proposes a 5G-enabled software-defined multicast network (5G-SDMNs), where software-defined networking (SDN) is exploited to dynamically manage multicast groups in 5G and mobile multicast environment. Also, mobile edge computing (MEC) is exploited to strengthen network control of 5G-SDMN. / National Open University of Nigeria