Group generated by abelian normal subgroups
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition
Symbol-free definition
A group is said to be generated by Abelian normal subgroups if there exists a collection of Abelian normal subgroups which together generate the group.
Examples
The dihedral group of size eight and the quaternion group are examples of non-Abelian groups generated by Abelian normal subgroups. While the former is generated by a cyclic normal subgroup of order 4 and a Klein-four group, the latter is generated by two cyclic normal subgroups.
Relation with other properties
Stronger properties
Weaker properties
- Nilpotent group (for finite groups)