# Elementary algebraic subset

From Groupprops

This article defines a property of subsets of groups

View other properties of subsets of groups|View properties of subsets of abelian groups|View subgroup properties

## Definition

A subset of a group is termed an **elementary algebraic subgroup** if there exists a word map and elements such that:

## Relation with other properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

algebraic subset | arbitrary intersection of finite unions of elementary algebraic subsets | |FULL LIST, MORE INFO | ||

unconditionally closed subset | closed for every topology making the group a T0 topological group | |FULL LIST, MORE INFO |