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2.64 (1966)

Solved

Does the set of nil-elements of a finite-dimensional linear group coincide with its locally nilpotent radical?

Contributor: B. I. Plotkin

Progress

Not always. The non-nilpotent 3-generator nilgroup of E. S. Golod constructed by an algebra over $\mathbb{Q}$ is residually torsion-free nilpotent; hence it is orderable and therefore it is embeddable into $\text{GL}_n$ over some skew field by Mal’cev’s theorem (V. A. Roman’kov, 1978).

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