A polycyclic group is a group 
having a finite subnormal series
whose factor groups 
are cyclic groups.
Equivalently, 
is solvable and every subgroup
of 
is finitely generated. A finitely
generated solvable group need not be polycyclic.
A group is virtually polycyclic if it has a polycyclic
subgroup of finite index.
See also
Cyclic Group,
Finitely Generated,
Quasi-Isometry,
Solvable
Group
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References
Segal, D. Polycyclic
Groups. Cambridge, England: Cambridge University Press, 1983.
Cite this as:
Weisstein, Eric W. "Polycyclic Group."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PolycyclicGroup.html
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