Real Classes of Finite Special Unitary Groups

2015/12/15 by Fry, Amanda Schaeffer, Vinroot, C. Ryan · 1 citation
#20E45 #20G40 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1512.04978

Abstract

We classify all real and strongly real classes of the finite special unitary group SU_n(q). Unless q ≡ 3 (mod 4) and n |4, the classification of real classes is similar to that of the finite special linear group SL_n(q). We relate strong reality in SU_n(q) to strong reality in the finite special orthogonal groups SO^±_n(q), and we classify real and strongly real classes in the last case for the group SO^±_n(q), when q is odd and n ≡ 2 (mod 4).

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