Series-isomorph-free subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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

Weaker properties