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Let $L$ and $H$ be finite-dimensional restricted Lie algebras over a perfectfield $\F$ such that $u(L)\cong u(H)$, where $u(L)$ is the restrictedenveloping algebra of $L$. We prove that if $L$ is $p$-nilpotent and abelian,then $L\cong H$. We deduce that if $L$ is abelian and $\F$ is algebraicallyclosed, then $L\cong H$. We use these results to prove the main result of thispaper stating that if $L$ is $p$-nilpotent, then $L/L'^p+\gamma_3(L)\congH/H'^p+\gamma_3(H)$.

Isomorphism invariants of restricted enveloping algebras