Series-isomorph-free subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed series-isomorph-free in $$G$$ if the following two conditions hold:


 * $$H$$ is a normal subgroup of $$G$$.
 * If $$K$$ is a normal subgroup of $$G$$ such that $$H \cong K$$ and $$G/H \cong G/K$$, then $$H = K$$.

Stronger properties

 * Weaker than::Isomorph-free subgroup
 * Weaker than::Normal-isomorph-free subgroup
 * Weaker than::Quotient-isomorph-free subgroup

Weaker properties

 * Stronger than::Action-isomorph-free subgroup
 * Stronger than::Characteristic subgroup