In this paper, we introduce the class of graded Ω-groups, which includes: groups; associative, conformal and vertex algebras; Lie algebras and graded algebras. The graded prime radical of a graded Ω-group is defined, and its elementwise characterization is given. It is shown that the graded prime radical of a graded Ω-groups with a finiteness condition coincides with the lower weakly solvable (in the Parfyonov sense) radical.

Weakened A. V. Mikhalev' sproblem about the prime radical of artinian Lie algebras is solved.

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