Series-equivalent subgroups

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This article defines an equivalence relation over the collection of subgroups within the same big group

Definition

Suppose $G$ is a group and $H$ and $K$ are normal subgroups. We say that $H$ and $K$ are series-equivalent if $H$ and $K$ are isomorphic groups and the quotient groups $G/H$ and $G/K$ are isomorphic groups.

Relation with other properties

Stronger properties

• Equal subgroups
• Conjugate subgroups
• Automorphic subgroups

Weaker properties

• Isomorphic subgroups
• Quotient-isomorphic subgroups