# Category:Definitions/Index of Subgroups

Jump to navigation
Jump to search

This category contains definitions related to Index of Subgroups.

Related results can be found in Category:Index of Subgroups.

Let $G$ be a group.

Let $H$ be a subgroup of $G$.

The **index of $H$ (in $G$)**, denoted $\index G H$, is the cardinality of the left (or right) coset space $G / H$.

### Finite Index

If $G / H$ is a finite set, then $\index G H$ is **finite**, and $H$ is **of finite index** in $G$.

### Infinite Index

If $G / H$ is an infinite set, then $\index G H$ is **infinite**, and $H$ is **of infinite index** in $G$.

## Pages in category "Definitions/Index of Subgroups"

The following 5 pages are in this category, out of 5 total.