# Difference between revisions of "Number of subgroups"

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==Definition== | ==Definition== |

## Latest revision as of 00:39, 20 August 2009

This article defines an arithmetic function on groups

View other such arithmetic functions

## Definition

Let be a group. The **number of subgroups** of is the number of subgroups that has.

Note that the number of subgroups of is finite if and only if is a finite group. `For full proof, refer: Finitely many subgroups iff finite`