Weak stem extension

Definition
Consider a group extension $$G$$ of $$N$$ and $$Q$$ as follows: $$G$$ is a group, $$N$$ is a normal subgroup of $$G$$, and $$Q$$ is the quotient group $$G/N$$.

We say that this group extension is a weak stem extension if the following hold:


 * 1) The extension is a central extension, i.e., $$N$$ is a normal subgroup of $$G$$.
 * 2) The associated homomorphism $$N \otimes N \to G^{\operatorname{ab}} \otimes N$$ is the trivial homomorphism.

Stronger properties of group extensions

 * Weaker than::stem extension

Weaker properties of group extensions

 * Stronger than::central extension