# Approximate subgroup

From Groupprops

This article defines a property of subsets of groups

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## Definition

Suppose is a positive integer. A finite subset of a group is termed a -approximate subgroup if it is a symmetric subset containing the identity element such that there exists a subset of of size at most such that the product of subsets coincides with the product of subsets :

where and

Note that any finite symmetric subset containing the identity element is always a -approximate subgroup, and is a 1-approximate subgroup if and only if it is a subgroup. The minimum value of for which is a -approximate subgroup describes how close is to being a subgroup.