Manoj Kumar Singh

The number of distinct element orders in a finite group

For a finite group $G$ let $\omega(G)$ denote its spectrum, the set of orders of its elements, and set $\eta(G)=|\omega(G)|$, the number of distinct element orders. The set $\omega(G)$ has been studied intensively, but its cardinality has received little systematic attention as an invariant in its own right. We develop...