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Elementarily characteristic 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]
This term is related to: model theory
View other terms related to model theory | View facts related to model theory


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This is a variation of characteristicity|Find other variations of characteristicity | Read a survey article on varying characteristicity

Contents

Definition

Symbol-free definition

A subgroup of a group is said to be elementarily characteristic or first-order characteristic if there is no subgroup that is elementarily equivalently embedded.

Relation with other properties