Bounded Engel elements in residually finite groups satisfying an identity.
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2021
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Let G be a m-generator residually finite group. We show that: 1) if every
ck-value in G is right n-Engel, then ckðGÞ is s-Engel for some
fk, m, ng-bounded number s; 2) if G satisfies an identity w 1 and G can
be generated by a commutator-closed set of left n-Engel elements, then G
has {m, n, w}-bounded class. 3) if G has a specific generating set X in which
some power of each element in X is a bounded left Engel, then G is virtu-
ally nilpotent.
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Lie algebras
Citação
BASTOS JÚNIOR, R. de A.; SILVEIRA, D. S. da. Bounded Engel elements in residually finite groups satisfying an identity. Communications in Algebra, v. 49, n. 6, p. 2556–2562, 2021. Disponível em: <https://www.tandfonline.com/doi/abs/10.1080/00927872.2021.1877295?journalCode=lagb20>. Acesso em: 29 abr. 2022.