Definition: Group A set g of elements and operator@ form a group if for all x,y in G, x@y is also ing(inclusion) there is an identityelement e such that for all x in G, e ax=x for all x in G, there is an inverse elemental such that x lax=e for all, y, z in G,(x@yaz=x@(y(@z)(associativity) abelian groups have the property: for all x,y in G, x@y=yax Note: sometimes the group operator may be denoted“*”Or“+”, the identity denoted “0or“1 and the inverse of x“-x2 Note 2: unless stated otherwise. we consider only abelian groupsDefinition: Group A set G of elements and operator @ form a group if: • for all x,y in G, x @ y is also in G (inclusion) • there is an identity element e such that for all x in G, e@x = x • for all x in G, there is an inverse element x -1 such that x-1@x = e • for all x,y,z in G, (x@y)@z = x@(y@z) (associativity) • abelian groups have the property: for all x,y in G, x@y = y@x Note: sometimes the group operator may be denoted “*” or “+”, the identity denoted “0” or “1” and the inverse of x “-x”. Note 2: unless stated otherwise, we consider only abelian groups