Root subgroup

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

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Root subgroup, all facts related to Root subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A subgroup $H$ of a group $G$ is termed a root subgroup if there exists an integer $n$ such that:

$H:=\{g\mid g^n=e\}$

Relation with other properties

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Variety-containing subgroup
1-endomorphism-invariant subgroup				|FULL LIST, MORE INFO
Existentially bound-word subgroup				|FULL LIST, MORE INFO
Quasiendomorphism-invariant subgroup				|FULL LIST, MORE INFO
Fully invariant subgroup				|FULL LIST, MORE INFO
Characteristic subgroup				|FULL LIST, MORE INFO
Normal subgroup				|FULL LIST, MORE INFO