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Multi-access Edge Computing (MEC) is an essential technology for expanding computing power of mobile devices,which can combine the Non-Orthogonal Multiple Access (NOMA) in the power domain to multiplex signals to improve spectral efficiency.We study the integration of the MEC with the NOMA to improve the computation service for the Beyond Fifth-Generation (BSG) and the Sixth-Generation (6G) wireless networks.This paper aims to minimize the energy consumption of a hybrid NOMA-assisted MEC system.In a hybrid NOMA system,a user can offload its task during a time slot shared with another user by the NOMA,and then upload the remaining data during an exclusive time duration served by Orthogonal Multiple Access (OMA).The original energy minimization problem is non-convex.To efficiently solve it,we first assume that the user grouping is given,and focuses on the one group case.Then,a multilevel programming method is proposed to solve the non-convex problem by decomposing it into three subproblems,i.e.,power allocation,time slot scheduling,and offloading task assignment,which are solved optimally by carefully studying their convexity and monotonicity.The derived solution is optimal to the original problem by substituting the closed expressions obtained from those decomposed sub-problems.Furthermore,we investigate the multi-user case,in which a close-to-optimal algorithm with low-complexity is proposed to form users into different groups with unique time slots.The simulation results verify the superior performance of the proposed scheme compared with some benchmarks,such as OMA and pureNOMA.