Variety-containing subgroup of finite group

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This article describes a property that arises as the conjunction of a subgroup property: variety-containing subgroup with a group property imposed on the ambient group: finite group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup of a finite group is termed a variety-containing subgroup of finite group if it satisfies the following equivalent conditions:

  1. It is a variety-containing subgroup of the whole group.
  2. It is a subhomomorph-containing subgroup of the whole group.
  3. It is a subisomorph-containing subgroup of the whole group.

Further information: Equivalence of definitions of variety-containing subgroup of finite group