A group 
such that the quotient group 
, where 
is the group center of
, is Abelian.
An equivalent condition is that the commutator
subgroup 
is contained in 
.
Metabelian Group
This entry contributed by Margherita Barile
Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Metabelian Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetabelianGroup.html