F. Oda

Deflation map and the sum of inverses of the element orders in finite groups

Let $G$ be a finite group. In this note, we construct an element ${\sigma}^G$ in the Burnside ring of $G$ over $\mathbb{Q}$, which gives a rational number $m(G)$ that is the sum of the inverses of the element orders in $G$, by using the deflation map ${\mathrm{Def}}^G_{G/N}$ induced by the $(G/N,G)$-biset $G/N$ for a n...