Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v = x the group G is nilpotent (rather than merely locally nilpotent).
An Engel condition for orderable groups
TORTORA, ANTONIO;TOTA, Maria
2015-01-01
Abstract
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) is locally nilpotent. We also show that in the particular case where v = x the group G is nilpotent (rather than merely locally nilpotent).File in questo prodotto:
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