Black Box Recognition of the Suzuki groups

2026/07/19 by John N. Bray, Henrik Bäärnhielm
Computer Science · Mathematics · #math.GR #cs.DS

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Abstract

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.

Citations

• A new method for recognising Suzuki groups

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