Lower Central Series of Baumslag–Solitar Groups

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We look at Baumslag–Solitar groups. Lower central series are given for residually nilpotent Baumslag–Solitar groups. For some Baumslag–Solitar groups that are not residually nilpotent, we find the intersection of all terms of the lower central series. Also we point out non-Abelian Baumslag–Solitar groups having lower central series of length 2. For some Baumslag–Solitar groups, a connection is found between an intersection of subgroups of finite index and an intersection of terms of the lower central series.

Original languageEnglish
Pages (from-to)281-294
Number of pages14
JournalAlgebra and Logic
Issue number4
Publication statusPublished - Sep 2020


  • Baumslag–Solitar groups
  • lower central series
  • residual nilpotency


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