Series-isomorph-free subgroup

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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 $H=K$.

Relation with other properties

Stronger properties

• Isomorph-free subgroup
• Normal-isomorph-free subgroup
• Quotient-isomorph-free subgroup

Weaker properties

• Action-isomorph-free subgroup
• Characteristic subgroup