Black Box Recognition of the Suzuki groups

We present a black box algorithm that constructs standard generators for the Suzuki groups $Sz(q)$, where $q = 2^{2m+1}$ for some $m > 0$.

The algorithm is one-sided Monte Carlo, with no false positives.

We also present a black box algorithm that performs constructive membership testing in $Sz(q)$, and writes an element as a straight line program in the standard generators.

Finally, we give a presentation for $Sz(q)$ that is efficient to verify.

The algorithms have been implemented in the computer algebra system Magma.