au^{-1} \) fixes all elements \( x' \in \tau(M) \), each \( \tau
  \gamma \tau^{-1} \) must be a \( \tau(M) \)-automorphism of \( L \).
  Thus \( \tau M^* \tau^{-1} \subseteq \tau(M)^* \).
</p>
<p>
  Similarly, for all \( \gamma' \in \tau(M)^* \), \( x \in M \), we
  use the notation \( x' = \tau(x) \in \tau(M) \) and get

  \[
  (\tau^{-1} \gamma' \tau)(x) = (\tau^{-1} \gamma')(x') = \tau^{-1}(x') = x.
  \]

  In the second equality above, we have used the fact that \( \gamma'
  \in \tau(M)^* \) which impl