Nikolaus Conference 2023

The Möbius function of locally finite posets is a classical tool in enumerative combinatorics. It is a generalization of the number-theoretic Möbius function and it has several applications in group theory. Referring to the Möbius function of a finite group \(G\), it is usual to consider the Möbius function \(\mu\) of the subgroup lattice of \(G\). But this is not the only Möbius function that has been studied in relation to a finite group. For many purposes it is sufficient to consider the poset of conjugacy classes of subgroups of \(G\) instead of the full subgroup lattice. In this case, the associated Möbius function is denoted by \(\lambda\). An interesting problem concerns the possibility to express \(\mu\) in terms of \(\lambda\).