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A group is a set of objects, sometimes referred to as <math>G \ </math>, and a rule of composition, <math>* \ </math>, such that

A group is a set of objects, sometimes referred to as <math>G \ </math>, and a rule of composition, <math>* \ </math>, such that

#. There is an element of <math>G \ </math>, call it <math>e \ </math>, such that for any <math>x \ </math> in <math>G \ </math>, <math>e*x = x*e = x \ </math>.  This element is called the identity of the group.  We write <math>x \in G \ </math> to mean that <math>x \ </math> is in <math>G \ </math>.

#There is an element of <math>G \ </math>, call it <math>e \ </math>, such that for any <math>x \ </math> in <math>G \ </math>, <math>e*x = x*e = x \ </math>.  This element is called the identity of the group.  We write <math>x \in G \ </math> to mean that <math>x \ </math> is in <math>G \ </math>.

 

#For any two <math>x, y \in G \ </math>, their composition <math>x*y \in G \ </math>.

#. For any two <math>x, y \in G \ </math>, their composition <math>x*y \in G \ </math>.

#For any three <math>x,y,z \in G, x*(y*z) = (x*y)*z \ </math>

 

#. For any three <math>x,y,z \in G, x*(y*z) = (x*y)*z \ </math>

[[Category:Algebra Terms]]

[[Category:Algebra Terms]]