Subquotient

This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
VIEW: Definitions built on this | Facts about this: (facts closely related to Subquotient, all facts related to Subquotient) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a complete list of semi-basic definitions on this wiki

Definition

Symbol-free definition

A subquotient of a group is a quotient of a subgroup of the group by a normal subgroup of that subgroup.

Definition with symbols

Let $G$ be a group. A subquotient of $G$ is a group of the form $H/N$ where $H$ is a subgroup of $G$ and $N$ is a normal subgroup of $H$.

Alternative names

Subquotients are also called:

• Involved groups
• Sections: This is not to be confused with the other use of the word section as a system of coset representatives.