On hypercentre-by-polycyclic-by-nilpotent groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 155-164.
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If {γ s+1 G} and {ζ s (G)} denote respectively the lower and upper central series of the group G, s0 an integer, and if γ s+1 G/(γ s+1 ζ s (G)) is polycyclic (resp. polycyclic-by-finite) for some s, then we prove that G/ζ 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.

Publié le :
DOI : 10.4171/RSMUP/19
Classification : 20, 00
Mots clés : Upper central series, lower central series, polycyclic group
Wehrfritz, B.A.F. 1

1 Queen Mary University of London, UK
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     title = {On hypercentre-by-polycyclic-by-nilpotent groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {155--164},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {141},
     year = {2019},
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Wehrfritz, B.A.F. On hypercentre-by-polycyclic-by-nilpotent groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 155-164. doi : 10.4171/RSMUP/19. http://www.numdam.org/articles/10.4171/RSMUP/19/

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