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21.123 (2026)

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Is it true that the extension of the A. Agrachev–R. Gamkrelidze construction of groups from pre-Lie rings in (J. Soviet Math., 17 (1981), 1650–1675) suggested in Definition 66 of (A. Smoktunowicz, J. Pure Appl. Algebra, 229, no. 12 (2025), 108128) produces groups from pre-Lie rings?

If this extended construction does give a group, then it also gives a brace, and so an affirmative answer to this question would have consequences for the theory of set-theoretic solutions of the Yang–Baxter equation and for the theory of braces.

Contributor: A. Smoktunowicz

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