A group G is a non-Empty Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=sEt">sEt upon which a Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=binary">binary opErator * is dEfinEd with thE following propErtiEs for all a,b,c in G: ClosurE: G is closEd undEr *, a*b in G AssociativE: * is associativE on G, (a*b)*c = a*(b*c) IdEntity: ThErE is an idEntity ElEmEnt E such that a*E = E*a = a. InvErsE: EvEry ElEmEnt has a uniquE invErsE a' such that a * a' = a' * a = E. ThE invErsE is usually writtEn with a supErscript -1. (1998-10-03)
