theorem Th5:
  a * A * A = a * A & a * (A * A) = a * A &
  A * A * a = A * a & A * (A * a) = A * a
proof
  thus a * A * A = a * (A * A) by GROUP_4:45
    .= a * A by GROUP_2:76;
  hence a * (A * A) = a * A by GROUP_4:45;
  thus A * A * a = A * a by GROUP_2:76;
  hence thesis by GROUP_4:46;
end;
