A family of non-FSZ finite symplectic groups

Abstract

Let $p$ be an odd prime with $p\equiv 1\mathrm{mod}4$. Then for any odd power $q$ of $p$ and a positive integer $j$ we show that the groups ${\text{Sp}}_{p^j+1}(q),{\text{PSp}}_{p^j+1}(q)$, and their Sylow $p$-subgroups are non-$FS{Z}_{p^j}$.

arXiv comment24 pages

References in corpus (4)

• Computing Higher Indicators for the Double of a Symmetric Group
• Eigenvalues of rotations and braids in spherical fusion categories
• Higher frobenius-schur indicators for drinfeld doubles of finite groups through characters of centralizers
• Some behaviors of FSZ groups under central products, central quotients, and regular wreath products