Special interest is attached to finitely-generated metabelian groups. These are all residually finite (see Residually-finite group) and satisfy the maximum condition (see Chain condition) for normal subgroups. An analogous property is shared by a generalization of these groups — the finitely-generated groups for which the quotient by an Abelian normal subgroup is polycyclic (see Polycyclic group).
In the Russian mathematical literature, by a metabelian group one sometimes means a nilpotent group of nilpotency class 2.
|||A.G. Kurosh, "The theory of groups" , 1–2 , Chelsea (1955–1956) (Translated from Russian)|
|||M.I. Kargapolov, J.I. [Yu.I. Merzlyakov] Merzljakov, "Fundamentals of the theory of groups" , Springer (1979) (Translated from Russian)|
|[a1]||D.J.S. Robinson, "A course in the theory of groups" , Springer (1980)|
Meta-Abelian group. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Meta-Abelian_group&oldid=31663