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Groupprops β

Intermediately normal-to-characteristic subgroup

Definition

Symbol-free definition

A subgroup of a group is termed intermediately normal-to-characteristic if it satisfies the following equivalent conditions:

Definition with symbols

A subgroup H of a group G is termed intermediately normal-to-characteristic in G if it satisfies the following equivalent conditions:

  • For any subgroup K of G containing H such that H is normal in K, H is characteristic in K.
  • H is characteristic in any subgroup of G contained in its normalizer N_G(H).

Formalisms

In terms of the in-normalizer operator

This property is obtained by applying the in-normalizer operator to the property: intermediately characteristic subgroup
View other properties obtained by applying the in-normalizer operator

A subgroup H \le G is intermediately normal-to-characteristic in G if and only if H is an intermediately characteristic subgroup in N_G(H).

Relation with other properties

Metaproperties