# Epigroup

From Groupprops

This is a variation of group|Find other variations of group | Read a survey article on varying group

This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup

View a complete list of semigroup properties

## Contents

## Definition

An **epigroup** (also termed a **group-bound semigroup**) is a semigroup with the property that every element has a power, such that the subsemigroup generated by that power, is a subgroup (i.e., a group under the induced multiplication).