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Groupprops β

Characteristic direct factor of abelian group

Definition

A subgroup H of a group G is termed a characteristic direct factor of G if the following equivalent conditions are satisfied:

  1. G is an abelian group and H is a characteristic direct factor of G (i.e., H is both a characteristic subgroup of G and a direct factor in G).
  2. G is an abelian group and H is a fully invariant direct factor of G (i.e., H is a fully invariant subgroup as well as a direct factor of G). See also equivalence of definitions of fully invariant direct factor for other equivalent formulations of this.

Equivalence of definitions

Further information: equivalence of definitions of characteristic direct factor of abelian group

Relation with other properties