Root subgroup

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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]

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 \}

When G is a finite group, a root subgroup is the same as a variety-containing subgroup of finite group.

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