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For context, $\phi_{f} $ and $\psi_{u} $ are two different automorphisms of the same group. I would like to know what the following notation, $\phi_{f}^{\psi_{u} } $ , is referring to? What does it mean to raise an automorphism to the power of another automorphism? I have checked, and it does not correspond to composing one with the other.

Thank you very much for your help

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    $\begingroup$ It’s hard to know without context, but if I had to guess it means conjugation (namely apply the right action of the automorphism group on itself by conjugation): $f^g= g^{-1} \circ f \circ g$. $\endgroup$
    – Andy Putman
    Dec 20 at 1:56

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