The structure of a finite group and the maximum $\pi$-index of its
elements
The structure of a finite group and the maximum $\pi$-index of its
elements
Given a set of primes $\pi$, the $\pi$-index of an element $x$ of a finite group $G$ is the $\pi$-part of the index of the centralizer of $x$ in $G$. If $\pi=\{p\}$ is a singleton, we just say the $p$-index. If the $\pi$-index of $x$ is equal to $p_1^{k_1}\ldots p^{k_s}$, …