Direct factor of characteristic subgroup

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This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: direct factor and characteristic subgroup
View other such compositions|View all subgroup properties

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


Symbol-free definition

A subgroup of a group is termed a direct factor of characteristic subgroup if it satisfies the following equivalent conditions:

In terms of the composition operator

The subgroup property of being a direct factor of characteristic subgroup is obtained by applying the composition operator to the subgroup properties of being a direct factor and of being characteristic.

Relation with other properties

Stronger properties

Weaker properties

Related properties