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ON FINITE-BY-NILPOTENT GROUPS
Published online by Cambridge University Press: 20 December 2019
Abstarct
Let γn = [x1,…,xn] be the nth lower central word. Denote by Xn the set of γn -values in a group G and suppose that there is a number m such that $|{g^{{X_n}}}| \le m$ for each g ∈ G. We prove that γn+1(G) has finite (m, n) -bounded order. This generalizes the much-celebrated theorem of B. H. Neumann that says that the commutator subgroup of a BFC-group is finite.
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- Research Article
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- Copyright
- © Glasgow Mathematical Journal Trust 2019
Footnotes
The first and third authors are members of INDAM. The fourth author was supported by CNPq-Brazil.
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