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Homesection of a group

## Primary tabs

# section of a group

A *section* of a group $G$ is
a quotient of a subgroup of $G$.
That is, a section of $G$ is a group of the form $H/N$,
where $H$ is a subgroup of $G$, and $N$ is a normal subgroup of $H$.

A group $G$ is said to be *involved in* a group $K$
if $G$ is isomorphic to a section of $K$.

The relation ‘is involved in’ is transitive, that is, if $G$ is involved in $K$ and $K$ is involved in $L$, then $G$ is involved in $L$.

Defines:

involved in

Synonym:

section, quotient of a subgroup

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

20F99*no label found*

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