Bounded Engel elements in residually finite groups satisfying an identity. Issue 6 (23rd January 2021)

• Record Type: Journal Article
• Authors: Bastos, Raimundo; Silveira, Danilo
• Is Part Of: Communications in algebra. Volume 49:Issue 6(2021)
• Page Start: 2556
• Page End: 2562
• Publication Date: 2021-01-23
• Subjects: Engel elements -- Lie algebras -- residually finite groups; 20E26 -- 20F40 -- 20F45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1877295
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let G be a m -generator residually finite group. We show that: 1) if every γk -value in G is right n -Engel, then γ k ( G ) is s -Engel for some { k, m, n } -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 virtually nilpotent.