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

Weaker properties

  • Isomorphic subgroups
  • Quotient-isomorphic subgroups