 ##  [Group](/group) 

  ##  [Group](https://mathlogic.quantumdictionary.io/group-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

An algebraic structure consisting of a set equipped with a single binary operation that is associative, has an identity element, and such that every element has an inverse with respect to the operation.

 
 ##  [Group](https://puremath.quantumdictionary.io/group-1) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A set equipped with a single binary operation that is associative, has an identity element, and in which every element has an inverse under that operation.

 
 ##  [Group](https://algebra.quantumdictionary.io/group-2) 

  
 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 
Definition

An algebraic structure (G, ·) consisting of a set G together with a binary operation · that is closed, associative, has an identity element e in G, and for every element g in G an inverse g^{-1} in G. The structure is considered up to equality of the set and operation, and homomorphisms preserve the operation.