la=XXEG, and x=a(mod =XXEG, and x*a1∈H} Let h=x*a-I. Then x=h*a, Thus a]={h*ah∈H Ha=h*aheh is called right coset of the subgroup h aH=fa*h heH is called left coset of the subgroup H Let [ H; be a subgroup of the group g;* anda∈G.Then (1)b∈ Ha iff b*a∈H (2 beah iff a1*b∈H[a]={x|xG, and xa(mod H)}={x|xG, and xa -1H} Let h=xa -1 . Then x=ha，Thus [a]={ha|hH} Ha={ha|hH} is called right coset of the subgroup H aH={ah|hH} is called left coset of the subgroup H Let [H;] be a subgroup of the group [G;], and aG. Then (1)bHa iff ba -1H (2)baH iff a-1bH