# Minimal characteristic subgroup

From Groupprops

This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Minimal characteristic subgroup, all facts related to Minimal characteristic subgroup) |Survey articles about this | Survey articles about definitions built on this

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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 nontrivial subgroup of a group is termed a **minimal characteristic subgroup** if it is a characteristic subgroup and does not properly contain any nontrivial characteristic subgroup.

## Formalisms

### In terms of the minimal operator

This property is obtained by applying the minimal operator to the property: nontrivial characteristic subgroup

View other properties obtained by applying the minimal operator