Contracharacteristic 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

Symbol-free definition

A subgroup of a group is termed a contracharacteristic subgroup if it satisfies the following equivalent conditions:

  1. Its characteristic closure in the whole group equals the whole group.
  2. It is not contained in any proper characteristic subgroup of the whole group.

Relation with other properties

Stronger properties

Facts