---
type: "concept"
title: "Order of an element of a group"
slug: "order-of-an-element-of-a-group"
language: "en"
translationGroupId: "cmraif69x000bnx01m21kplxx"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "sequoia"
---

The order of an element $x$ of a group $(G,\cdot)$ is the smallest positive integer $k$ such that $x^k=e$ where $e$ is the neutral element from $G$. For instance, the order of $e$ is $1$.

If this integer does not exist (in the case of infinite groups), we say that the order is infinite.