Title: On the uniqueness of roots in virtually nilpotent groups
Authors: Descheemaeker, An ×
Malfait, Wim #
Issue Date: Nov-1999
Publisher: Springer verlag
Series Title: Mathematische zeitschrift vol:232 issue:3 pages:487-503
Abstract: After revisiting the concept of the torsion subgroup of a group with respect to a set of prime numbers P (as introduced by Ribenboim), we show that, for all p in P, p-th roots are unique in a virtually nilpotent group if and only if P-roots are unique in both its Fitting subgroup and its Fitting quotient. This more general notion of torsion also turns out to be sufficient to understand completely the kernel of the P-localization homomorphism of a virtually nilpotent group. Using this result, we characterize the finitely generated virtually nilpotent groups such that, when dividing out the P-torsion subgroup, P-roots exist and are unique in the resulting quotient.
ISSN: 0025-5874
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
Mathematics, Campus Kulak Kortrijk
× corresponding author
# (joint) last author

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