Contracharacteristic subgroup

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


 * 1) Its defining ingredient::characteristic closure in the whole group equals the whole group.
 * 2) It is not contained in any proper characteristic subgroup of the whole group.

Stronger properties

 * Weaker than::Contranormal subgroup

Facts

 * Every subgroup is contracharacteristic in its normal closure: In particular, every subgroup of a group is a contracharacteristic subgroup of a normal subgroup.