質問: Let $L$ be a finite lattice with minimum $\hat{0}$ and maximum $\hat{1}$. The Möbius function $\mu$ for $L$ is defined recursively by: for $\forall a,b \in L$ with $a
回答: The answer to your question is ``yes". Something more general was proved by Hawkes, Isaacs and \"Ozaydin in a 1989 paper in the Rocky Mountain Journal of Mathematics. CORRECTION: As Sebastien Palcoux notes below, this result is due to Kratzer and Th\'evenaz More precise results for the groups $PSL_2(p)$ were known to Philip Hall, and $PSL_2(q)$ was handled by Martin Downs, as were the Suzuki groups. Some results on symmetric groups appear in a paper of mine, and other classes of ``small" almost simple groups are addressed in my thesis, (Sorry, it is a postscript file and some non-mathematical pages are repeated.)