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An Engel condition for orderable groups (1402.5247v1)
Published 21 Feb 2014 in math.GR
Abstract: Let m,n be positive integers, v a multilinear commutator word and w=vm. 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).
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