Algebraic subgroup

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

WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with algebraic group

Definition

A subgroup of a group is termed an algebraic subgroup if it is an algebraic subset of the group, i.e., it is an intersection of finite unions of elementary algebraic subsets.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
marginal subgroup		marginal implies algebraic		|FULL LIST, MORE INFO
weakly marginal subgroup				|FULL LIST, MORE INFO
c-closed subgroup	centralizer of a subset.	c-closed implies algebraic		|FULL LIST, MORE INFO
universally bound-word subgroup				|FULL LIST, MORE INFO
finite subgroup				|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
unconditionally closed subgroup	closed in any T0 topological group structure on the whole group.			|FULL LIST, MORE INFO