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A subalgebra

\mathfrak{h}

of a Lie algebra

\mathfrak g

is said to have the

\gamma

property with respect to a scalar product

{\langle \cdot,\cdot \rangle}

given on

{\mathfrak g}

{X \in \mathfrak{h}}

implies

{\langle [X,Y],X\rangle =0}

for all

{Y \in \mathfrak g}

. Prove that the maximum dimension of

{\gamma}

-property subalgebras of a given

{2}

step nilpotent Lie algebra with respect to a scalar product is independent of the selection of the scalar product.
Proposed by Péter Nagy Tibor

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