On hypercentre-by-polycyclic-by-nilpotent groups

  • B.A.F. Wehrfritz

    Queen Mary University of London, UK
On hypercentre-by-polycyclic-by-nilpotent groups cover
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If {γs+1G}\{\gamma^{s+1}G\} and {ζs(G)}\{\zeta_{s}(G)\} denote respectively the lower and upper central series of the group GG, s0s\geq 0 an integer, and if γs+1G/(γs+1ζs(G))\gamma^{s+1}G/(\gamma^{s+1}\cap \zeta_{s}(G)) is polycyclic (resp. polycyclic-by-finite) for some ss, then we prove that G/ζ2s(G)G/\zeta_{2s}(G) is polycyclic (resp. polycyclic-by-finite). The corresponding result with polycyclic replaced by finite was proved in 2009 by G.A. Fernández-Alcober and M. Morigi. We also present an alternative approach to the latter.

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B.A.F. Wehrfritz, On hypercentre-by-polycyclic-by-nilpotent groups. Rend. Sem. Mat. Univ. Padova 141 (2019), pp. 155–164

DOI 10.4171/RSMUP/19