Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon:


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

A group $ (G,\diamond)$ is a set $ G$ together with a binary operation $ \diamond$:

$\displaystyle \diamond: G \times G \longmapsto G\,,

that is, a uniquely determined element $ a \diamond b \in G$ is assigned to each pair of elements $ (a,b)$ where $ a,b \in G$. Furthermore the operation must satisfy the following requirements (group axioms):

A group is called commutative or Abelian group, if its operation is commutative:

$\displaystyle \forall a,b \in G \quad a \diamond b = b \diamond a

If it is clear which operation is used, then often only $ G$ is written instead of $ (G,\diamond)$.
(Authors: Burkhardt/Höllig/Hörner)

[Examples] [Links]

  automatically generated 3/31/2005