The Möbius function of PSU(3, 2sup{2supn}) - Zini, Giovanni (Ars mathematica contemporanea, 2019)
Let ?$G$? be the simple group ?$PSU(3, 2^{2^n}),\ n > 0$?. For any subgroup ?$H$? of ?$G$?, we compute the Möbius function ?$μ_L(H, G)$? of ?$H$? in the subgroup lattice ?$L$? of ?$G$?, and the Möbius function ?$μ_{\bar L}(H, G)$? of ?$H$? in the poset ?$\bar L$? of conjugacy classes of subgroups of ?$G$?. For any prime ?$p$?, we provide the Euler characteristic of the order complex of the poset of non-trivial ?$p$?-subgroups of ?$G$?.
Keywords: Möbius function; Möbiusova funkcija; mreža podgrup; subgroup lattice; unitarne grupe; unitary groups