On Residually Finite Groups with Engel-like Conditions. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Bastos, Raimundo
• Is Part Of: Communications in algebra. Volume 44:Issue 10(2016)
• Page Start: 4177
• Page End: 4184
• Publication Date: 2016-10-02
• Subjects: Engel elements -- Residually finite groups; 20F45 -- 20E26; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1087014
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract : Let m, n be positive integers. Suppose that G is a residually finite group in which for every element x ∈ G there exists a positive integer q = q ( x ) ≤ m such that x q is left n -Engel. We show that G is locally virtually nilpotent. Further, let w be a multilinear commutator and G a residually finite group in which for every product of at most 896 w -values x there exists a positive integer q = q ( x ) dividing m such that x q is left n -Engel. Then w ( G ) is locally virtually nilpotent.