Invariance under any derivation with partial divided Leibniz condition powers is transitive
From Groupprops
This article gives the statement, and possibly proof, of a Lie ring property (i.e., Lie subring invariant under any derivation with partial divided Leibniz condition powers) satisfying a Lie ring metaproperty (i.e., transitive Lie subring property)
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Statement
Suppose is a Lie ring and
are Lie subrings of
with
contained in
. Suppose
is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in
. Similarly, suppose
is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in
.
Then, is a Lie subring invariant under any derivation with partial divided Leibniz condition powers in
.