The M\"{o}bius Function of the Suzuki Groups

TL;DR

This paper calculates the M"obius function for the subgroup lattice of Suzuki groups, enabling enumeration of specific normal subgroups in related Hecke groups with Suzuki group quotients.

Contribution

It provides the first explicit computation of the M"obius function for Suzuki groups' subgroup lattice, facilitating subgroup enumeration in related algebraic structures.

Findings

M"obius function explicitly computed for Suzuki groups

Enumeration formulas for normal subgroups in Hecke groups derived

Applications to subgroup classification in algebraic groups

Abstract

We compute the M\"obius function for the subgroup lattice of the simple Suzuki group $Sz(q)$; this is used to enumerate normal subgroups of certain Hecke groups with quotients isomorphic to $Sz(q)$.