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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
 General Mathematics
 Applied Mathematics
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Dive into the research topics of 'Left 3Engel elements of odd order in groups'. Together they form a unique fingerprint.Projects
 1 Finished

Left 3Engel Elements in Groups
Engineering and Physical Sciences Research Council
1/08/17 → 31/05/22
Project: Research council
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Gunnar Traustason
 Department of Mathematical Sciences  Head of Department
Person: Research & Teaching