Abstract
In this note we analyse the analogy betweenm-potent andp-central restricted Lie algebras andp-groups. For restricted Lie algebras the notion ofm-potency has stronger implications than forp-groups (Theorem A). Every finite-dimensional restricted Lie algebra is isomorphic tofor some finite-dimensionalp-central restricted Lie algebra(Proposition B). In particular, for restricted Lie algebras there does not hold an analogue of J.Buckley's theorem. Forpodd one can characterise powerful restricted Lie algebras in terms of the cup product map in the same way as for finitep-groups (Theorem C). Moreover, thep-centrality of the finite-dimensional restricted Lie algebra has a strong implication on the structure of the cohomology ringH•(,) (Theorem D).
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