A metabelian group is a group that possesses a normal subgroup such that and are both abelian. Equivalently, is metabelian if and only if the commutator subgroup is abelian. Equivalently again, is metabelian if and only if it is solvable of length at most .
Subgroups (http://planetmath.org/Subgroup), quotients (http://planetmath.org/QuotientGroup) and (unrestricted) direct products of metabelian groups are also metabelian. In other words, metabelian groups form a variety (http://planetmath.org/VarietyOfGroups); they are, in fact, the groups in which for all elements , , and .
|Date of creation||2013-03-22 15:36:42|
|Last modified on||2013-03-22 15:36:42|
|Last modified by||yark (2760)|