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Groupprops β

Groups embeddable as normal subgroups in a finite group with isomorphic complements

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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 complements if there exists a finite group A with normal subgroups B,C and subgroups D,E such that:

  • B is isomorphic to G.
  • B and D are permutable complements: in particular, A is an internal semidirect product of B and D.
  • C is isomorphic to H.
  • C and E are permutable complements: in particular, A is an internal semidirect product of C and E.
  • D is isomorphic to E.

Relation with other relations