Groups embeddable as normal subgroups in a finite group with isomorphic quotient groups

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Definition

Suppose G and H are finite groups. We say that G and H are embeddable as normal subgroups in a finite group with isomorphic quotient groups if there exists a group A with normal subgroups B,C such that:

  • B is isomorphic to G.
  • C is isomorphic to H.
  • A/B is isomorphic to A/C.

Relation with other relations

Stronger relations

Weaker relations