Lie algebras and torsion groups with identity
We prove that a finitely generated Lie algebra L such that (i) every commutator in generators is ad-nilpotent, and (ii) L satisfies a polynomial identity, is nilpotent. As a corollary we get that a finitely generated residually- p torsion group whose pro- p completion satisfies a pro- p identity is...
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| Veröffentlicht in: | Journal of combinatorial algebra 2017-01, Vol.1 (3), p.289-340 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove that a finitely generated Lie algebra
L
such that (i) every commutator in generators is ad-nilpotent, and (ii)
L
satisfies a polynomial identity, is nilpotent. As a corollary we get that a finitely generated residually-
p
torsion group whose pro-
p
completion satisfies a pro-
p
identity is finite. |
|---|---|
| ISSN: | 2415-6302 2415-6310 |
| DOI: | 10.4171/jca/1-3-2 |