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- W200058295 abstract "We say that a group G has finite lower central depth if the lower cen- tral series of G stabilises after a finite number of steps, that is, G has finite lower central depth if and only if gk (G) 4 gk 1 1 (G) for some positive integer k . The least integer k such that gk (G) 4 gk 1 1 (G), is called the depth of G. We denote by V the class of groups which has finite lower central depth. If k is a positive integer, we denote by V k the class of all groups having finite lower central depth at most k . Let G be a finitely generated soluble group. In this note we prove, G is finite-by-nilpotent if and only if in every infinite set of ele- ments of G there exist two distinct elements x , y such that ax , ybV , and G is finite by a group in wich every two generator subgroup is nilpotent of class at most k if and only if in every infinite set of elements of G there exist two dis- tinct elements x , y such that ax , ybV k ." @default.
- W200058295 created "2016-06-24" @default.
- W200058295 creator A5029156204 @default.
- W200058295 date "2004-01-01" @default.
- W200058295 modified "2023-09-27" @default.
- W200058295 title "Characterisation of finitely generated soluble finite-by-nilpotent groups" @default.
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