Definition:Gro叩p A set g of elements and operator@ form a group if for ally in g,x@y is also ing(inclusion) there is an identity element e such that for all x in g, e(ax=X for all x in G, there is an inverse element such that x.@x=e for allx,y, z in G, (x@y@z=x@(yaz)(associativity) abelian groups have the property: for all x,y inG, x@y=y@x Note: sometimes the group operator may be denoted“*”or“+”, the identity denoted 0or“1 and the inverse ofx“-x” Note 2: unless stated otherwise, we consider only abelian roupsDefinition: 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