Algebraic 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]
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