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 for each g a 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.
ON FINITE-BY-NILPOTENT GROUPS
Detomi E.;
2021
Abstract
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 for each g a 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.File in questo prodotto:
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