Variety-dominating 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 variety-dominating if there exists a subvariety \mathcal{V} of the variety of groups such that:

  • H \in \mathcal{V}.
  • If K \le G is such that K \in \mathcal{V}, there exists g \in G such that gKg^{-1} \le H.

Relation with other properties

Stronger properties

Weaker properties

Facts