Abstract
Let G be a group and let x ε G be a left 3Engel element of odd order. We show that x is in the locally nilpotent radical of G. We establish this by proving that any finitely generated sandwich group, generated by elements of odd orders, is nilpotent. This can be seen as a group theoretic analog of a wellknown theorem on sandwich algebras by Kostrikin and Zel’manov. We also give some applications of our main result. In particular, for any given word w = w(x1, . . ., xn) in n variables, we show that if the variety of groups satisfying the law w 3 = 1 is a locally finite variety of groups of exponent 9, then the same is true for the variety of groups satisfying the law (x 3 n +1 w 3 ) 3 = 1.
Original language  English 

Pages (fromto)  19211927 
Number of pages  7 
Journal  Proceedings of the American Mathematical Society 
Volume  147 
Issue number  5 
Early online date  18 Jan 2019 
DOIs  
Publication status  Published  31 May 2019 
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
Profiles

Gunnar Traustason
 Department of Mathematical Sciences  Deputy Head of Department
Person: Research & Teaching