theorem
  center G is normal Subgroup of G
proof
  now
    let a;
    thus a * center G c= center G * a
    proof
      let x be object;
      assume x in a * center G;
      then consider b such that
A1:   x = a * b and
A2:   b in center G by GROUP_2:103;
      x = b * a by A1,A2,Th77;
      hence thesis by A2,GROUP_2:104;
    end;
  end;
  hence thesis by GROUP_3:118;
end;
