# Proper characteristic subgroup

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This article is about a basic definition in group theory. The article text may, however, contain advanced material.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Proper characteristic subgroup, all facts related to Proper characteristic subgroup) |Survey articles about this | Survey articles about definitions built on this

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: proper subgroup and characteristic subgroup

View other subgroup property conjunctions | view all subgroup properties

## Definition

### Symbol-free definition

A subgroup of a group is termed a **proper characteristic subgroup** if it satisfies *both* these conditions:

- It is a proper subgroup
- It is a characteristic subgroup